A method for constructing exact solutions of nonlinear evolution equation with variable coefficients

Abstract

A function transformation method for constructing exact solutions of the variable coefficient nonlinear evolution equations is proposed. The method together with the the second kind of elliptic equation and the symbolic computation system Mathematica is used to construct the new exact Jacobi elliptic function solutions, the degenerated soliton-like solutions and trigonometric function solutions of the composed KdV equation with forced variable coefficients.

Fusion, fission, and annihilation of complex waves for the (2+1)-dimensional generalized Calogero—Bogoyavlenskii—Schiff system

“…As is well known, to search for the solitary wave solutions of a nonlinear physical model, we can apply several different approaches. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] One of the most efficient methods of finding soliton excitations of a physical model is the so-called mapping approach. [24,[28][29][30][31][32][33][34][35][36][37][38] Previously, Mei and Zhang have obtained exact traveling wave solutions for the Gross-Pitavskii system with the Riccari equation (ξ = a 0 + a 1 ξ + a 2 ξ 2 ) expansion method.…”

Constructing infinite sequence exact solutions of nonlinear evolution equations

“…Case II Infinite sequence peak soliton solutions of generalized pentavalent KdV equation Case II(a) Peak solitary wave solutions of hyperbolic function type Substituting infinite sequence solutions determined by the known solutions (30) and Bäcklund transformation (37) for the first kind of elliptic function into Eq. ( 56), we can construct the infinite sequence peak solitary 110203-7…”

“…Case II(b) Peak solitary wave solutions of triangle function type Taking infinite sequence solutions determined by the known solutions (29) and Bäcklund transformation (37) for the first kind of elliptic function into Eq. ( 56), we can find the infinite sequence peak solitary wave solutions of triangle function type to the generalized pentavalent KdV equation as follows:…”

Complex solutions and novel complex wave localized excitations for the (2+1)-dimensional Boiti—Leon—Pempinelli system

“…[1][2][3] The exact solutions of such equations play an important role in nonlinear science, especially in nonlinear physics, since they can provide much physical information and more insight into the physical aspects of the problem and thus lead to applications. [4][5][6][7][8][9] The exact solutions of NPDEs are an interesting and popular topic in nonlinear mathematical physics, and various methods for obtaining the exact solutions of nonlinear systems have been proposed, for example, the bilinear method, the standard Painlevé truncated expansion, the method of "coalescence of eigenvalue" or "wavenumbers", the homogenous balance method, the hyperbolic function method, the Jacobian elliptic method, the variable separation method, the (G /G)-expansion method, [10][11][12][13][14][15][16][17][18][19][20][21][22] and the mapping method. [23][24][25][26][27][28][29][30][31][32] The mapping approach is a kind of classic, efficient, and well-developed method to solve nonlinear evolution equations.…”