The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

Abstract

It is renowned that Hirota–Satsuma–Ito (HSI) equation is widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended to diversify problems in natural phenomena and give admirable contributions by applying the generalized exponential rational function method (GERFM). With the aid of symbolic calculations, various constraints on the free parameters are given, while classes of wave solutions are explicitly constructed from the coefficients of the combined non-linear and dissipative terms. After specifying values for free parameters, singular, periodic singular and anti-kink waves are demonstrated in 3D figures to exhibit different kinds of wave propagations. The fact that parameters directly influence the wave amplitude and speed of traveling waves is illustrated. The derived results are innovative and have important applications in the current field of mathematical physics research. Eventually, we show that generalized exponential rational function method is effective and straightforward to solve higher-order and high-dimensional non-linear evolution equations.

Bifurcation and Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation

“…This typically involves converting the blackNLPDE into ordinary differential equations. [33,46,50,52] Existing methods can be split into two categories. The first type of approach creates a limited set of exact solutions by simple computations, whereas the second approach, such the symbolic computation method, requires complex computations, but produces abundant wave solutions.…”