N -Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation

Advances in Mathematical Physics

Chen

et al. 2017

Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

Section: Introductionmentioning

confidence: 99%

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Advances in Mathematical Physics

Chen

et al. 2017

“…Numerical method is a supplement of the nonisospectral problem. [23−25] For the nonisospectral GSK equation, N -soliton solutions were obtained by Zhou et al, [26] and the Wronskian solution and soliton resonance were also discussed by Zhou et al [27] The nonisospectral BKP equation and other soliton equations were derived by Chen et al [28] and Deng [29] provided the bilinear form of the nonisospectral BKP equation by using the Hirota method. [30] The nonisospectral BKP equation is given by…”

Section: Introductionmentioning

confidence: 99%

Double Wronskian Solution and Soliton Properties of the Nonisospectral BKP Equation

Chan

et al. 2016

Commun. Theor. Phys.

Self Cite

“…The Novikov equation also enjoys two other important properties of the CH equation; it admits peakon solutions and the Cauchy problem [26]. We all know that nonlocal integrable systems have attracted much attention in different nonlocal nonlinear equations, for example, the nonlocal nonlinear Schrödinger equation [27,28], the nonlocal modified KdV systems [29], the (2+1)-dimensional KdV equation [30], KP equation [31], (2+1)-dimensional Sawada-Kotera equation [32,33], nonlocal symmetry for the gKP equation [34], nonlocal symmetry of the (2+1)-dimensional breaking soliton equation [35], (2+1)dimensional Gardner equation [36], and Drinfeld-Sokolov-Satsuma-Hirota system [37]. Recently, Lou introduced Alice-Bob (AB) models to study two-place physical problems [38].…”

mentioning

confidence: 99%

Peakon Solutions of Alice-Bob b-Family Equation and Novikov Equation

Advances in Mathematical Physics

Xiong

2019

By requiring B=P^sT^dA and substituting u=A+B into the b-family equation and Novikov equation, we can obtain Alice-Bob peakon systems, where P^s and T^d are the arbitrary shifted parity transformation and delayed time reversal transformation, respectively. The nonlocal integrable Camassa-Holm equation and Degasperis-Procesi equation can be derived from the Alice-Bob b-family equations by choosing different parameters. Some new types of interesting solutions are solved including explicit one-peakons, two-peakons, and N-peakons solutions.