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Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation

Year 2021, Volume 11, Issue 1, 13 - 24, 30.06.2021

Abstract

In this article, the wave solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation, which is investigated as a mathematical model, are get by using the modified exponential function method (MEFM). When the solution functions found are analyzed, it is determined that hyperbolic and trigonometric functions, which are periodic functions, are also obtained in their rational functions. Two-dimensional, three-dimensional, contour and density graphs representing the wave solutions of the mathematical model found were plotted by determining appropriate parameters.

References

  • Baskonus H M & Bulut H (2015). On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves in Random and Complex Media 25(4): 720-728
  • Bulut H, Akturk T & Gurefe Y (2015). An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings 1648(1): 370014
  • Bulut H (2017). Application of the modified exponential function method to the Cahn-Allen equation. AIP Conference Proceedings 1798(1): 020033
  • Chen Y & Yan Z (2005). New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals 26(2): 399-406
  • Du X-H, (2010). An irrational trial equation method and its applications. Pramana - Journal of Physics 75(3): 415-422
  • Erdogan F, Sakar M G & Saldır O (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences 5(1): 425-436
  • Gurefe Y, Misirli E, Sonmezoglu A & Ekici M (2013). Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation 219(10): 5253-5260
  • He J-H & Wu X-H (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30(3): 700-708
  • Manukure S, Chowdhury A & Zhou Y (2019). Complexiton solutions to the asymmetric Nizhnik-Novikov-Veselov equation. International Journal of Modern Physics B 33(11): 1950098
  • Naher H & Abdullah F A (2013). New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation. AIP Advances 3(3): 032116
  • Nuruddeen R I & Nass A M (2018). Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method. Journal of Taibah University for Science 12(3): 309-314
  • Peng Y-Z (2005). A class of doubly periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation. Physics Letters A 337(1-2): 55-60
  • Ren Y-J & Zhang H-Q (2006). A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Chaos, Solitons and Fractals 27: 959-979
  • Sakar M, Yeskindirova M & Saldir O (2020). Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations. Theoretical and Applied Mechanics Letters 10(5): 333-342
  • Wazwaz A-M (2007). Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation 190(1): 633-640
  • Wazwaz A-M (2010). Multiple soliton solutions for the (2+ 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. Nonlinear Analysis: Theory, Methods & Applications 72(3-4): 1314-1318
  • Xu G-Q & Deng S-F (2016). Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation. The European Physical Journal Plus 131: 385

(2+1)-boyutlu Nizhnik-Novikov-Veselov denkleminin dalga çözümlerinin analizi

Year 2021, Volume 11, Issue 1, 13 - 24, 30.06.2021

Abstract

Bu makalede matematiksel model olarak incelenen (2+1)-boyutlu Nizhnik-Novikov-Veselov denkleminin dalga çözümleri modifiye edilmiş üstel fonksiyon metodu (MEFM) kullanılarak elde edilmiştir. Bulunan çözüm fonksiyonları incelendiğinde periyodik fonksiyonlar olan hiperbolik ve trigonometrik fonksiyonların ayrıca rasyonel fonksiyonların da elde edildiği belirlenmiştir. Bulunan matematiksel modelin dalga çözümlerini temsil eden iki boyutlu, üç boyutlu, kontur ve yoğunluk grafikleri uygun parametreler belirlenerek çizilmiştir.

References

  • Baskonus H M & Bulut H (2015). On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves in Random and Complex Media 25(4): 720-728
  • Bulut H, Akturk T & Gurefe Y (2015). An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings 1648(1): 370014
  • Bulut H (2017). Application of the modified exponential function method to the Cahn-Allen equation. AIP Conference Proceedings 1798(1): 020033
  • Chen Y & Yan Z (2005). New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals 26(2): 399-406
  • Du X-H, (2010). An irrational trial equation method and its applications. Pramana - Journal of Physics 75(3): 415-422
  • Erdogan F, Sakar M G & Saldır O (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences 5(1): 425-436
  • Gurefe Y, Misirli E, Sonmezoglu A & Ekici M (2013). Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation 219(10): 5253-5260
  • He J-H & Wu X-H (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30(3): 700-708
  • Manukure S, Chowdhury A & Zhou Y (2019). Complexiton solutions to the asymmetric Nizhnik-Novikov-Veselov equation. International Journal of Modern Physics B 33(11): 1950098
  • Naher H & Abdullah F A (2013). New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation. AIP Advances 3(3): 032116
  • Nuruddeen R I & Nass A M (2018). Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method. Journal of Taibah University for Science 12(3): 309-314
  • Peng Y-Z (2005). A class of doubly periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation. Physics Letters A 337(1-2): 55-60
  • Ren Y-J & Zhang H-Q (2006). A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Chaos, Solitons and Fractals 27: 959-979
  • Sakar M, Yeskindirova M & Saldir O (2020). Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations. Theoretical and Applied Mechanics Letters 10(5): 333-342
  • Wazwaz A-M (2007). Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation 190(1): 633-640
  • Wazwaz A-M (2010). Multiple soliton solutions for the (2+ 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. Nonlinear Analysis: Theory, Methods & Applications 72(3-4): 1314-1318
  • Xu G-Q & Deng S-F (2016). Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation. The European Physical Journal Plus 131: 385

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Tolga AKTÜRK (Primary Author)
ORDU ÜNİVERSİTESİ
0000-0002-8873-0424
Türkiye


Çağlar KUBAL
ORDU ÜNİVERSİTESİ
0000-0003-2958-7514
Türkiye

Publication Date June 30, 2021
Published in Issue Year 2021, Volume 11, Issue 1

Cite

Bibtex @research article { ordubtd928242, journal = {Ordu Üniversitesi Bilim ve Teknoloji Dergisi}, issn = {2146-6440}, eissn = {2146-6459}, address = {}, publisher = {Ordu University}, year = {2021}, volume = {11}, pages = {13 - 24}, doi = {}, title = {Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation}, key = {cite}, author = {Aktürk, Tolga and Kubal, Çağlar} }
APA Aktürk, T. & Kubal, Ç. (2021). Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation . Ordu Üniversitesi Bilim ve Teknoloji Dergisi , 11 (1) , 13-24 . Retrieved from https://dergipark.org.tr/en/pub/ordubtd/issue/63218/928242
MLA Aktürk, T. , Kubal, Ç. "Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation" . Ordu Üniversitesi Bilim ve Teknoloji Dergisi 11 (2021 ): 13-24 <https://dergipark.org.tr/en/pub/ordubtd/issue/63218/928242>
Chicago Aktürk, T. , Kubal, Ç. "Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation". Ordu Üniversitesi Bilim ve Teknoloji Dergisi 11 (2021 ): 13-24
RIS TY - JOUR T1 - Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation AU - Tolga Aktürk , Çağlar Kubal Y1 - 2021 PY - 2021 N1 - DO - T2 - Ordu Üniversitesi Bilim ve Teknoloji Dergisi JF - Journal JO - JOR SP - 13 EP - 24 VL - 11 IS - 1 SN - 2146-6440-2146-6459 M3 - UR - Y2 - 2021 ER -
EndNote %0 Ordu University Journal of Science and Tecnology Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation %A Tolga Aktürk , Çağlar Kubal %T Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation %D 2021 %J Ordu Üniversitesi Bilim ve Teknoloji Dergisi %P 2146-6440-2146-6459 %V 11 %N 1 %R %U
ISNAD Aktürk, Tolga , Kubal, Çağlar . "Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation". Ordu Üniversitesi Bilim ve Teknoloji Dergisi 11 / 1 (June 2021): 13-24 .
AMA Aktürk T. , Kubal Ç. Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Ordu Üniversitesi Bilim ve Teknoloji Dergisi. 2021; 11(1): 13-24.
Vancouver Aktürk T. , Kubal Ç. Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation. Ordu Üniversitesi Bilim ve Teknoloji Dergisi. 2021; 11(1): 13-24.
IEEE T. Aktürk and Ç. Kubal , "Analysis of wave solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equation", Ordu Üniversitesi Bilim ve Teknoloji Dergisi, vol. 11, no. 1, pp. 13-24, Jun. 2021

DANIŞMA KURULU

Dr. Mushtaq Ahmed - University of Science & Technology- Bannu
Dr. Francesso CALABRESE - Dipartmento di Colture Arbaee, Universitate di Palermo
Dr. Hicham Zazou - University Ibn Zohr - Agadir/Morocco
Dr. Shunguan LII -  College of Horticulture South Chine Agricultural Univ.
Dr. Fouad GUENFOUD - Université de Tlemcen- Tlemcen/Algérie
Dr. Zehruni MESSAOUDI - Department arboniculture-Viticulture Ecole Nationale d Agriculture de Meknes
Dr. Khuram Ali Khan - University of Sargodha- Punjab
Dr. Zoubir DAHMANI - University of Mostaganem- Algeria
Dr. Osamu TERAI - Nagasaki Fruit Tree Experiment
Dr. Mohammed Wasim Siddiqui - Bihar Agricultural University, Sabour
Dr. Jose M. LEITAO - Universidade do Algarue
Prof. Dr. Borris KRISKA - Mendel University
Prof. Dr. Abdullah MENZEK - Atatürk Üniversitesi
Prof. Dr. Âdem ERSOY - Çukurova Üniversitesi
Prof. Dr. Adnan ERDAĞ - Adnan Menderes Üniversitesi
Prof. Dr. Ali İrfan İLBAŞ - Erciyes Üniversitesi
Prof. Dr. Aliye ALTUNDAŞ -  Gazi Üniversitesi
Prof. Dr. Ahmet CANSIZ - İstanbul Teknik Üniversitesi
Prof. Dr. Ahmet DURMUŞ - Karadeniz Teknik Üniversitesi
Prof. Dr. Ahmet KAZANKAYA - Yüzüncü Yıl Üniversitesi
Prof. Dr. Ayhan SARIOĞLUGİL - Ondokuz Mayıs Üniversitesi
Prof. Dr. Ahmet UYANIK - Ondokuz Mayıs Üniversitesi
Prof. Dr. Ahmet YARTAŞI - Çankırı Karatekin Üniversitesi
Prof. Dr. Burhan ARSLAN - Namık Kemal Üniversitesi
Prof. Dr. Celal TUNCER - Ondokuz Mayıs Üniversitesi
Prof. Dr. Cemil YAPAR - Ordu Üniversitesi
Prof. Dr. Cevdet COŞKUN - Giresun Üniversitesi
Prof. Dr. Cumhur ÇÖKMÜŞ - Ankara Üniversitesi
Prof. Dr. Dürdane KOLONKAYA - Hacettepe Üniversitesi
Prof. Dr. Ertunç GÜNDÜZ - Hacettepe Üniversitesi
Prof. Dr. Fahri YAVUZ - Atatürk Üniversitesi
Prof. Dr. Ferhan TÜMER - Atatürk Üniversitesi
Prof. Dr. Fikri BALTA - Ordu Üniversitesi
Prof.Dr.F. Ekmel TEKİNTAŞ - Adnan Menderes Üniversitesi
Prof. Dr. Gençağa PÜRÇEK - Karadeniz Teknik Üniversitesi
Prof. Dr. Halil KÜTÜK - Ondokuz Mayıs Üniversitesi
Prof. Dr. Halim ÖZDEMİR - Sakarya Üniversitesi
Prof. Dr. Halis AYGÜN - Kocaeli Üniversitesi
Prof. Dr. Hasan GÜMÜŞ - Ondokuz Mayıs Üniversitesi
Prof. Dr. Hasan SEÇEN - Atatürk Üniversitesi
Prof. Dr. İhsan ÜNVER - Karadeniz Teknik Üniversitesi
Doç. Dr. İlkay ŞİŞMAN - Sakarya Üniversitesi
Doç. Dr. İ. Yasin ERDOĞAN - Bingöl Üniversitesi
Prof. Dr. Lütfi ÖZYÜZER - İzmir Yüksek Teknolojileri Üniversitesi
Prof. Dr. Mehmet AKBAŞ - Karadeniz Teknik Üniversitesi
Prof.Dr. Mehmet Cengiz KAYACAN - Süleyman Demirel Üniversitesi
Prof. Dr. Mehmet ÇAKIROĞLU - Ondokuz Mayıs Üniversitesi
Prof. Dr. Mehmet GAVGALI - Atatürk Üniversitesi
Prof. Dr. Mehmet TÜMER - Kahramanmaraş Sütçü İmam Üniversitesi
Prof. Dr. Mehmet ÜLKER - Yüzüncü Yıl Üniversitesi
Prof. Dr. Metin HÜSEM - Karadeniz Teknik Üniversitesi
Prof. Dr. Mustafa BÜYÜKYILMAZ - Namık Kemal Üniversitesi
Prof. Dr. Mustafa ÇALIŞKAN - Gazi Üniversitesi
Prof. Dr. Ömer AKBULUT - Atatürk Üniversitesi
Prof. Dr. Ö. İrfan KÜFREVİOĞLU - Atatürk Üniversitesi
Prof. Dr. Refik KESKİN - Sakarya Üniversitesi
Prof. Dr. Rüştü HATİPOĞLU - Çukurova Üniversitesi
Prof.Dr. Sadri ŞEN - Atatürk Üniversitesi
Prof.Dr. S. Zeki BOSTAN - Ordu Üniversitesi
Prof. Dr. Sebahattin TÜZEMEN - Atatürk Üniversitesi
Prof. Dr. Sinan UYANIK - Harran Üniversitesi
Prof. Dr. Suat AKBULUT - Atatürk Üniversitesi
Prof. Dr. Şenol EREN - Ondokuz Mayıs Üniversitesi
Prof. Dr. Ş. Metin KARA - Ordu Üniversitesi
Prof. Dr. Tarık YARILGAÇ - Ordu Üniversitesi