Soliton solutions and traveling wave solutions of the two-dimensional generalized nonlinear Schrödinger equations
Faculty of Nuclear Sciences and Physical Engineering, CTU, Prague, Czech Republic
2 Department of General and Theoretical Physics, LN Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
3 JSC National Company “Kazakhstan Gharysh Sapary”, Nur-Sultan, Kazakhstan
Accepted: 18 October 2021
Published online: 30 October 2021
In this paper, the two-dimensional generalized nonlinear Schrödinger equations are introduced with the Lax pair. The existence of the Lax pair defines integrability for the partial differential equation, so the two-dimensional generalized nonlinear Schrödinger equations are integrable. Related to this development was the understanding that certain coherent structures called solitons play a basic role in nonlinear phenomena as fluid mechanics, nonlinear optics relativity, and lattice dynamics. Via the Hirota bilinear method, bilinear forms of the two-dimensional generalized nonlinear Schrödinger equations are obtained. Based on which one- and two-soliton solutions are derived. Furthermore, to find traveling wave solutions the extended tanh method is applied. Through 2D and 3D plots, the dynamical behavior of the obtained solutions is studied. The generalized form of the nonlinear Schrödinger equations has a mathematical and physical interest because a fundamental model in the field of nonlinear science. The used methods are quite useful in the solution of nonlinear partial differential equations.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021