Breather-wave, periodic-wave and traveling-wave solutions for a (2 + 1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation for an incompressible fluid

In this paper, the investigation is conducted on a (2 + 1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation for an incompressible fluid. Via the Riemann theta function, periodic-wave solutions are derived, and breather-wave solutions are constructed with the aid of the extended homoclinic test approach. Based on the polynomial expansion method, several traveling-wave solutions are derived. Besides, we observe that the amplitude of the breather keeps unchanged during the propagation and the traveling wave which is kink shaped propagates stably. Furthermore, we analyze the transition between the periodic-wave and soliton solutions, which implies that the periodic-wave solutions tend to the soliton solutions via a limiting procedure.

[1]  Bang-Qing Li,et al.  Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation , 2020, Appl. Math. Comput..

[2]  Onur Alp Ilhan,et al.  Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics , 2020, Communications in Theoretical Physics.

[3]  C. Dai,et al.  Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation , 2020 .

[4]  D. Lu,et al.  Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma , 2020 .

[5]  Min Li,et al.  Multi-pole solutions and their asymptotic analysis of the focusing Ablowitz–Ladik equation , 2020, Physica Scripta.

[6]  T. Xia,et al.  Lump and Lump–Kink Soliton Solutions of an Extended Boiti–Leon–Manna–Pempinelli Equation , 2020 .

[7]  Zhong-Zhou Lan,et al.  Periodic, breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics , 2019, Appl. Math. Lett..

[8]  Min Li,et al.  General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system. , 2019, Chaos.

[9]  M. Kaplan.  Two different systematic techniques to find analytical solutions of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation , 2018, Chinese Journal of Physics.

[10]  Tian-Tian Zhang,et al.  Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation , 2018, Appl. Math. Lett..

[11]  A. Abdikian.  Cylindrical fast magnetosonic solitary waves in quantum degenerate electron-positron-ion plasma , 2018 .

[12]  Mukesh Kumar,et al.  Soliton solutions of BLMP equation by Lie symmetry approach , 2017, Comput. Math. Appl..

[13]  Pan Wang,et al.  Soliton solutions for the fifth-order Kaup–Kupershmidt equation , 2017, Physica Scripta.

[14]  Dipankar Kumar,et al.  The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics , 2017 .

[15]  Yaning Tang,et al.  Interaction solutions between lump and other solitons of two classes of nonlinear evolution equations , 2017 .

[16]  Shou‐Fu Tian,et al.  Quasiperiodic waves, solitary waves and asymptotic properties for a generalized (3 + 1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation , 2017 .

[17]  M. Kaplan,et al.  The Auto-Bäcklund transformations for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation , 2017 .

[18]  A. Seadawy.  Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves , 2017 .

[19]  Yi-Tian Gao,et al.  Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas , 2016 .

[20]  Shou-Fu Tian,et al.  On periodic wave solutions with asymptotic behaviors to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics , 2016, Comput. Math. Appl..