Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Resolution of these functional equations leads to the τ-function and addition formulae t...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

Abstract: By means of a simple transformation, we have shown that the generalized-Zakharov equations, the coupled nonlinear Klein-Gordon-Zakarov equations, the GDS, DS and GZ equations and generalized Hirota-Satsuma coupled KdV system can be reduced to the ellipticlike equations. Then, the extended projective Riccati equation expansion method is used to obtain a series of solutions including ne...

In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

Abstract: In this paper, the homotopy perturbation method (HPM) is applied to obtain approximate solutions to three systems of nonlinear wave equations, namely, two component evolutionary system of a homogeneous KdV equations of order 3 (type I) as well as (type II), and the generalized coupled Hirota Satsuma KdV. The numerical results show that this method is a powerful tool for solving system...

An extended mapping method is used to drive some new exact travelling wave solutions of nonlinear evolution equations arising in physics,namely,generalized Hirota-Satsuma coupled KdV system and coupled Maccaris equations.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases have...

In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition (SDM), then use to solve generalized Hirota-Satsuma Coupled kdv (H-SC kdv) systems also applied STM, find approximate solutions of system one. Then compare way exact solitary solutions. Clarifying best through tables d...