A generalized and improved G′/G -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-KuznetsovBenjamin-Bona-Mahony ZKBBM equation and the strain wave equation in microstructured solids. Abundant exact travelling wave s...

A ( $$3+1$$ )-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton solutions are constructed. In the process of degeneration solutions, T-breathers derived by taking complexication method. Then rogue will emerge during breathers parameter limit Through full N-soliton, M-lump based long-wave...

The KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed n...

In this letter, we established a traveling wave solution by using cosine function algorithm for Gardnerequation and (2+1)-dimensional breaking soliton system. The cosine method is used to obtain theexact solution.

The existence of soliton solutions is one of the main features of nonlinear wave models solvable by means of the inverse scattering method. Each of these models has associated a particular type of soliton; however, solitons always share a series of common properties: they behave as classical particles and their scattering processes may be interpreted as a succession of paired collisions in whic...

In this paper, by using the bifurcation method of dynamical systems, we derive traveling wave solutions nonlinear equation UUτyy − UyUτy + U2Uτ 3Uy = 0. Based on relationship between Novikov and equation, present parametric representations smooth nonsmooth soliton for with cubic nonlinearity. These contain peaked soliton, W-shaped periodic solutions. Our work extends some previous results.

A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...

In this paper, the modified simple equation method is used to construct exact periodic and soliton solutions of some nonlinear partial differential equations. Exact solutions of the nonlinear Schrödinger equation, the Hamiltonian amplitude equation, Klein-Gordon equation in 1+2 dimension, the coupled Klein-Gordon equation, the (2 + 1)-dimensional long-wave-short-wave resonance interaction equat...

The integral sign with a backslash denotes the principal value. The constant σ is taken to be ±1. For positive (negative) σ, the equation is called the defocusing (focusing) INLS equation. Originally, the defocusing INLS equation was discovered by carrying out a reductive perturbation method for the ILW equation [8]. It describes the long–term evolution of quasi–harmonic wave packets whose wave...

We present a systematic and formal approach toward finding solitary wave solutions of non-linear evolution and wave equations f r cn the real exponential solutions of the underlying linear equations. The physical concept is one of the mixing of these elementary solutions through the non-linearities in the system. In the present paper the emphasis is, however, on the mathematical aspects, i.e. t...