Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma

Abstract

The extended Zakharov-Kuznetsov (eZK) equation for the magnetized two-ion-temperature dusty plasma is studied in this paper. With the help of Hirota method, bilinear forms and N-soliton solutions are given, and soliton propagation is graphically analyzed. We find that the soliton amplitude is positively related to the nonlinear coefficient A, while inversely related to the dispersion coefficients B and C. We obtain that the soliton amplitude will increase with the mass of the jth dust grain and the average charge number residing on the dust grain decreased, but the soliton amplitude will increase with the equilibrium number density of the jth dust grain increased. Upon the introduction of the periodic external forcing term, both the weak and developed chaotic motions can occur. Difference between the two chaotic motions roots in the inequality between the nonlinear coefficient l2 and perturbed term h1. The developed chaos can be weakened with B or C decreased and A increased. Periodic motion of the perturbed eZK equation can be observed when there is a balance between l2 and h1.

On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

“…Besides, for (1), multi-periodic solutions [12], variable-separation solutions [13,14], and soliton-like solutions [15] have been obtained. Conversely, integrable versions of the NLEEs usually have the soliton solutions [16][17][18][19][20]. A soliton is a solitary wave which preserves its velocity and shape after the interaction [7], i.e., the soliton can be considered as a quasiparticle [21,22].…”

Higher-Order Rogue Waves for a Fifth-Order Dispersive Nonlinear Schrödinger Equation in an Optical Fibre

“…Moreover, some effects of the higher-order terms on the first-order rogue waves have been investigated [30][31][32][33][34]. Rational W-shaped solitons on a continuouswave background for the Sasa-Satsuma equation have been obtained, and the stability properties of solutions have been investigated via the DT [30], with the relevant issues in [31,32].…”

“…Rational W-shaped solitons on a continuouswave background for the Sasa-Satsuma equation have been obtained, and the stability properties of solutions have been investigated via the DT [30], with the relevant issues in [31,32]. Solutions on the non-zero background for the Sasa-Satsuma equation have been derived, such as the breathers and rogue wave solutions, and the condition to form the rogue wave has been obtained via the limiting processes [33].…”

Dynamic structures of nonlinear ion acoustic waves in a nonextensive electron–positron–ion plasma

“…Zhen et al [4] studied dynamic behavior of the quantum ZK equation in dense quantum magnetoplasma. Zhen et al [5] also studied soliton solution and chaotic motion of the extended ZK equations in a magnetized dusty plasmas with Maxwellian hot and cold ions.…”

“…Both are related to astonishing properties of nonlinear systems, the strange attractor is linked to the idea of chaos [1] in a system with small number of degree of freedom, while the solitons appear in the systems with the large number of degree of freedom. The study of interesting solitonic structures, periodic solution, and chaotic structures [2][3][4][5] in plasma dynamics is very important and curious. Therefore, the investigation of various structures like solitonic, periodic, quasi-periodic, and chaotic in nonlinear plasma dynamics is a growing research field of plasma physics.…”