We consider N-soliton solutions of the KP equation, (−4ut + uxxx + 6uux)x + 3uyy = 0 . An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. The Nsoliton solutions include all possible resonant interactions among those line solitons. We then classify those N-soliton solutions by defining a pair of Nnumbers (n,n) w...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

This work concerns itself on two new coupled mKdV systems, the first with time-dependent coefficients, and the second with constant coefficients. The soliton ansatz will be used for the first system to obtain 1-bright soliton solution. The simplified form of the bilinear method will be used to derive multiple-soliton solutions and multiple singular soliton solutions for the second coupled mKdV ...

In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota’s bilinear method. Oneand two-bright-dark soliton solutions are explicitly presented for two-component semidiscrete NLS equation; two-bright-one-dark, and one-bright-two-dark soliton solutions are also given explicitly for three-component se...

In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota’s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented. Keywords—three-wave method; (3+1)-dimensional Soliton equation; Hirota’s bilinear form.

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

The bifurcation method of planar systems and simulation method of differential equations are employed to investigate loop soliton solutions of the reduced Ostrovsky equation (ROE). The parameter representation of loop soliton solutions of the ROE are obtained. The planar graphs of the loop soliton solutions is shown under the some parameter. These results are supplement to investigate the ROE.

Nonlinear evolution wave equations (NEEs) are partial differential equations (PDEs) involving first or second order derivatives with respect to time. Such equations have been intensively studied for the past few decades [1-3] and several new methods to solve nonlinear PDEs either numerically or analytically are now available. Hirota's bilinear method is a powerful tool for obtaining a wide clas...

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line soli...

In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x = 3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the r...