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 KdV equation with small dispersion is a model for the formation and propagation of dispersive shock waves. Dispersive shock waves are characterized by the appearance of modulated oscillations nearby the breaking point. The modulation in time and space of the amplitude, the frequencies and the wave-numbers of these oscillations is described by the g-phase Whitham equations. We study the init...

In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Rie...

Abstract: In this paper, we study the application of the known generalized (G ′ G )-expansion method for seeking more exact travelling solutions solutions and soliton solutions of the Kaup-Kupershmidt equation and the (2+1) dimensional breaking soliton equation. As a result, we come to the conclusion that the traveling wave solutions for the two non-linear equations are obtained in three arbitr...

The (2+1)-dimensional “universal” variable separation formula (Tang, Lou and Zhang, Physical Review E 66, 046601 (2002)) is extended to a more general form for some (2+1)-dimensional integrable systems. Various independent arbitrary functions have been included in the extended formula. Starting from the universal formula and its extended form, a new type of solitons, foldons, is studied both an...

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each the preceding equations, a Galilean type transformation between these $u_2$ previously known $u_2^{\prime}$ generated zero seed is given. We present several explicit formulas single-soliton for $u_2...

The ( 2 + 1 )-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known id="M3"> soliton associated Ablowitz-Kaup-Newell-Segur hierarchy. Then, based on finite-order expansion matrix, a hyperelliptic Riemann surface and Abel-Jacobi coordinates...