Nonlinear wave propagation in plasma and spin chains: New analytical solutions
Öz
In this study, we investigated two significant nonlinear evolution models, namely the New Hamiltonian Amplitude Equation (NHAE) and the Heisenberg Ferromagnetic Spin Chain Equation (HFSCE), which are used to describe wave propagation phenomena arising in plasma physics, nonlinear optics, fluid dynamics, magnetism, and spin chain systems. Investigating the exact solutions of these models is important for understanding the physical mechanisms of nonlinear wave interactions and predicting complex dynamical behaviors in applied sciences. To this end, the governing partial differential equations were transformed into nonlinear ordinary differential equations through a traveling wave transformation, and the -expansion method was employed to construct new exact analytical solutions. As a result, several previously unreported wave structures were obtained for both models. The solutions for the NHAE include rational-exponential forms, periodic waves, and localized complex profiles with phase-dependent amplitude modulation. The obtained solutions for the HFSCE represent oscillatory spin-wave modes, kink-type transitions, and exponentially varying magnetic excitations with modulated envelopes. These findings demonstrate that both equations possess rich families of bounded, singular, periodic, and modulated traveling waves, reflecting the diverse nonlinear dynamics supported by these models. Three-dimensional surface plots and contour illustrations are provided to visualize the propagation characteristics of the derived solutions. A comparison with earlier studies confirms that the obtained results are new, more general in several parameter regimes, and extend the existing literature by presenting additional exact wave structures through an efficient analytical framework.
Anahtar Kelimeler
New Hamiltonian amplitude equation, Heisenberg ferromagnetic spin chain equation, (m+1/G')-expansion method, Exact wave solution
Kaynakça
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