Bilinear form, auto-Bäcklund transformations and kink solutions of a $$(3+1)$$-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid

Chen, Yu-Qi; Tian, Bo; Shen, Yuan; Zhou, Tian-Yu

doi:10.1007/s12043-024-02740-3

Pramana - J Phys

2024

DOI: 10.1007/s12043-024-02740-3

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Bilinear form, auto-Bäcklund transformations and kink solutions of a $$(3+1)$$-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid

Yu-Qi Chen,

Bo Tian,

Yuan Shen

et al.

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Newly formed solitary wave solutions and other solitons to the (3+1)-dimensional mKdV–ZK equation utilizing a new modified Sardar sub-equation approach

Hamid,

Kumar

2024

Mod. Phys. Lett. B

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In this paper, we are going to investigate the (3+1)-dimensional nonlinear modified Korteweg–de Vries-Zakharov–Kuznetsov (mKdV–ZK) equation, which governs the behavior of weakly nonlinear ion acoustic waves in magnetized electron–positron plasma. By taking advantage of the newly proposed modified Sardar sub-equation method, we derive a comprehensive set of exact soliton solutions to the mKdV–ZK equation. Additionally, we provide graphical representations of the solutions, including 2D, 3D, and contour plots, to visualize the characteristics and features of these nonlinear wave structures. These solutions encompass a diverse range of wave patterns, including traveling waves, bright solitons, periodic waves, dark–bright solitons, lump-type solitons, and multi-soliton solutions. The obtained solutions provide valuable insights into the nonlinear behaviors and dynamics exhibited by the mKdV–ZK equation. The success of the new modified Sardar sub-equation method in obtaining a diverse range of solutions for the [Formula: see text]-dimensional mKdV–ZK equation highlights its potential for applications in the analysis of various nonlinear systems in plasma physics and beyond. Also, the study reviewed the superiority of the modified method compared to the Sardar sub-equation method.

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Newly formed solitary wave solutions and other solitons to the (3+1)-dimensional mKdV–ZK equation utilizing a new modified Sardar sub-equation approach

Hamid,

Kumar

2024

Mod. Phys. Lett. B

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show abstract

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Bilinear form, auto-Bäcklund transformations and kink solutions of a $$(3+1)$$-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid

Cited by 1 publication

References 29 publications

Newly formed solitary wave solutions and other solitons to the (3+1)-dimensional mKdV–ZK equation utilizing a new modified Sardar sub-equation approach

Newly formed solitary wave solutions and other solitons to the (3+1)-dimensional mKdV–ZK equation utilizing a new modified Sardar sub-equation approach

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