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Year 2017, Volume: 5 Issue: 1, 179 - 189, 01.01.2017

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References

  • A. Bansal and R. K. Gupta, On certain new exact solutions of the (2+1)-dimensional Calogero-Degasperis equation via symmetry approach, Int. J. Nonlinear Sci. 13 (2012), no. 4, 475–481.
  • F. Calogero and A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform. I, Nuovo Cimento B (11) 32 (1976), no. 2, 201–242.
  • F. Calogero and A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform. II, Nuovo Cimento B (11) 39 (1977), no. 1, 1–54.
  • G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer, New York, 1974.
  • G. Bluman,J.D. Cole The general similarity solution of the heat equation." J. Math Mech 42.
  • G. Bluman et al., Similarity: generalizations, applications and open problems, J. Engrg. Math. 66 (2010), no. 1-3, 1–9.
  • G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Applied Mathematical Sciences, 81, Springer, New York, 1989.
  • J.-F. Zhang et al., Folded solitary waves and foldons in the (2+1)-dimensional breaking soliton equation, Chaos Solitons Fractals 20 (2004), no. 3, 523–527.
  • L. V. Ovsiannikov, Group Analysis of Differential Equations, translated from the Russian by Y. Chapovsky, translation edited by William F. Ames, Academic Press, New York, 1982.
  • O. Bogoyavlenskij, Restricted Lie point symmetries and reductions for ideal magnetohydrodynamics equilibria, J. Engrg. Math. 66 (2010), no. 1-3, 141–152.
  • P. J. Olver, Applications of Lie Groups to Differential Equations, second edition, Graduate Texts in Mathematics, 107, Springer, New York, 1993.
  • Sachin Kumar and Y.K. Gupta (2014), “Generalized Invariant Solutions for Spherical Symmetric Non-Conformally Flat Fluid Distributions of Embedding Class One." International Journal of Theoretical Physics, 53: 2041-2050.
  • Y.-H. Tian, H.-L. Chen and X.-Q. Liu, Reduction and new explicit solutions of (2+1)-dmensional breaking soliton equation, Commun. Theor. Phys. (Beijing) 45 (2006), no. 1, 33–35.
  • X. Da-Quan, Symmetry reduction and new non-traveling wave solutions of (2+1)-dimensional breaking soliton equation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 8, 2061–2065.
  • X. Geng and C. Cao, Explicit solutions of the 2+1-dimensional breaking soliton equation, Chaos Solitons Fractals 22 (2004), no. 3, 683–691.
  • Y. K. Gupta, Pratibha and S. Kumar, Some nonconformal accelerating perfect fluid plates of embedding class 1 using similarity transformations, Internat. J. Modern Phys. A 25 (2010), no. 9, 1863–1879.
  • Z.-Y. Yan and H.-Q. Zhang, Constructing families of soliton-like solutions to a (2+1)-dimensional breaking soliton equation using symbolic computation, Comput. Math. Appl. 44 (2002), no. 10-11, 1439–1444.

Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation

Year 2017, Volume: 5 Issue: 1, 179 - 189, 01.01.2017

Abstract


References

  • A. Bansal and R. K. Gupta, On certain new exact solutions of the (2+1)-dimensional Calogero-Degasperis equation via symmetry approach, Int. J. Nonlinear Sci. 13 (2012), no. 4, 475–481.
  • F. Calogero and A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform. I, Nuovo Cimento B (11) 32 (1976), no. 2, 201–242.
  • F. Calogero and A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform. II, Nuovo Cimento B (11) 39 (1977), no. 1, 1–54.
  • G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer, New York, 1974.
  • G. Bluman,J.D. Cole The general similarity solution of the heat equation." J. Math Mech 42.
  • G. Bluman et al., Similarity: generalizations, applications and open problems, J. Engrg. Math. 66 (2010), no. 1-3, 1–9.
  • G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Applied Mathematical Sciences, 81, Springer, New York, 1989.
  • J.-F. Zhang et al., Folded solitary waves and foldons in the (2+1)-dimensional breaking soliton equation, Chaos Solitons Fractals 20 (2004), no. 3, 523–527.
  • L. V. Ovsiannikov, Group Analysis of Differential Equations, translated from the Russian by Y. Chapovsky, translation edited by William F. Ames, Academic Press, New York, 1982.
  • O. Bogoyavlenskij, Restricted Lie point symmetries and reductions for ideal magnetohydrodynamics equilibria, J. Engrg. Math. 66 (2010), no. 1-3, 141–152.
  • P. J. Olver, Applications of Lie Groups to Differential Equations, second edition, Graduate Texts in Mathematics, 107, Springer, New York, 1993.
  • Sachin Kumar and Y.K. Gupta (2014), “Generalized Invariant Solutions for Spherical Symmetric Non-Conformally Flat Fluid Distributions of Embedding Class One." International Journal of Theoretical Physics, 53: 2041-2050.
  • Y.-H. Tian, H.-L. Chen and X.-Q. Liu, Reduction and new explicit solutions of (2+1)-dmensional breaking soliton equation, Commun. Theor. Phys. (Beijing) 45 (2006), no. 1, 33–35.
  • X. Da-Quan, Symmetry reduction and new non-traveling wave solutions of (2+1)-dimensional breaking soliton equation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 8, 2061–2065.
  • X. Geng and C. Cao, Explicit solutions of the 2+1-dimensional breaking soliton equation, Chaos Solitons Fractals 22 (2004), no. 3, 683–691.
  • Y. K. Gupta, Pratibha and S. Kumar, Some nonconformal accelerating perfect fluid plates of embedding class 1 using similarity transformations, Internat. J. Modern Phys. A 25 (2010), no. 9, 1863–1879.
  • Z.-Y. Yan and H.-Q. Zhang, Constructing families of soliton-like solutions to a (2+1)-dimensional breaking soliton equation using symbolic computation, Comput. Math. Appl. 44 (2002), no. 10-11, 1439–1444.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Vishakha Jadaun This is me

Sachin Kumar This is me

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Jadaun, V., & Kumar, S. (2017). Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation. New Trends in Mathematical Sciences, 5(1), 179-189.
AMA Jadaun V, Kumar S. Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation. New Trends in Mathematical Sciences. January 2017;5(1):179-189.
Chicago Jadaun, Vishakha, and Sachin Kumar. “Lie Point Symmetries and Invariant Solutions of (2+1)- Dimensional Calogero Degasperis Equation”. New Trends in Mathematical Sciences 5, no. 1 (January 2017): 179-89.
EndNote Jadaun V, Kumar S (January 1, 2017) Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation. New Trends in Mathematical Sciences 5 1 179–189.
IEEE V. Jadaun and S. Kumar, “Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 179–189, 2017.
ISNAD Jadaun, Vishakha - Kumar, Sachin. “Lie Point Symmetries and Invariant Solutions of (2+1)- Dimensional Calogero Degasperis Equation”. New Trends in Mathematical Sciences 5/1 (January 2017), 179-189.
JAMA Jadaun V, Kumar S. Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation. New Trends in Mathematical Sciences. 2017;5:179–189.
MLA Jadaun, Vishakha and Sachin Kumar. “Lie Point Symmetries and Invariant Solutions of (2+1)- Dimensional Calogero Degasperis Equation”. New Trends in Mathematical Sciences, vol. 5, no. 1, 2017, pp. 179-8.
Vancouver Jadaun V, Kumar S. Lie point symmetries and invariant solutions of (2+1)- dimensional Calogero Degasperis equation. New Trends in Mathematical Sciences. 2017;5(1):179-8.