Bilinear Bäcklund transformations, kink periodic solitary wave and lump wave solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili equation

The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equation are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.

Download Full-text

Auto-Bäcklund transformations and solitary wave solutions for the nonlinear evolution equation

Optical and Quantum Electronics ◽

10.1007/s11082-017-1291-1 ◽

2017 ◽

Vol 50 (1) ◽

Cited By ~ 3

Author(s):

Melike Kaplan ◽

Mehmet Naci Ozer

Keyword(s):

Solitary Wave ◽

Evolution Equation ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Bäcklund Transformations ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

Backlund Transformations

Download Full-text

Breather wave, rogue wave and lump wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

Modern Physics Letters B ◽

10.1142/s0217984918502238 ◽

2018 ◽

Vol 32 (20) ◽

pp. 1850223 ◽

Cited By ~ 7

Author(s):

Ming-Zhen Li ◽

Bo Tian ◽

Yan Sun ◽

Xiao-Yu Wu ◽

Chen-Rong Zhang

Keyword(s):

Wave Velocity ◽

Water Waves ◽

Rogue Wave ◽

Rogue Waves ◽

Dispersion Effect ◽

Wave Solutions ◽

Weak Perturbation ◽

Petviashvili Equation ◽

Nonlinearity Effect ◽

Lump Wave

Under investigation in this paper is a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in a fluid. Via the Hirota method and symbolic computation, the lump wave, breather wave and rogue wave solutions are obtained. We graphically present the lump waves under the influence of the dispersion effect, nonlinearity effect, disturbed wave velocity effects and perturbed effects: Decreasing value of the dispersion effect can lead to the range of the lump wave decreases, but has no effect on the amplitude. When the value of the nonlinearity effect or disturbed wave velocity effects increases respectively, lump wave’s amplitude decreases but lump wave’s location keeps unchanged. Amplitudes of the lump waves are independent of the perturbed effects. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity. When the value of the dispersion effect decreases, range of the rogue wave increases. When the value of the nonlinearity effect or disturbed wave velocity effects decreases respectively, rogue wave’s amplitude decreases. Value changes of the perturbed effects cannot influence the rogue wave.

Download Full-text