Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation

Quasiperiodic waves and asymptotic behavior for the nonisospectral and variable-coefficient KdV equation

“…where α j = p j 2πi , σ j = γ j +πτ j j 2πi , A 12 = −2πτ 12 , j = 1, 2, and A 12 being as those give in (19). We can expand the solution of the system (38) has the following form …”

“…In 1980s, Nakamura proposed a convenient way to construct a kind of quasiperiodic solutions of nonlinear equation by using the Riemann theta function [14], it gives us a way to obtain periodic wave solutions of NLEEs conveniently. Further Fan, Ma, and one of the authors have extended this method to investigate the breaking soliton equation, ANNV, MNNV, generalized KdV, and the Boussinesq equations respectively [15][16][17][18][19].…”

Multiple wave solutions and auto-Bäcklund transformation for the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation

“…Over the past decades, many kinds of powerful methods have been proposed to find solutions, which contain the Hirota's bilinear method [1], the Exp-function method [2], the Painlevé analysis [3], the Bäcklund transformation method [4,5] and the Wronskian technique [6][7][8][9]. At present the Exp-function method proposed by He and Wu in Ref.…”

Exact Solutions and Wronskian Formulation for a New Form of the (3+1)-Dimensional BKP Equation

“…Some methods have been developed to obtain the exact solutions, such as the Bäcklund transformation method [1], the Hirota's bilinear method [2], the Painlevé analysis [3] and the Wronskian technique [4,5]. It is well known that the bilinear method first proposed by Hirota provides us with a comprehensive approach to construct exact solutions [2].…”