Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Abstract

A large member of lump chain solutions of the (2+1)-dimensional BKP equation are constructed by means of the τ-function in form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

Highly Dispersive Optical Solitons with Quadratic-Cubic Nonlinear form of Self-Phase Modulation by Sardar Sub-Equation Approach

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Nonlocal symmetries, nonlocally related systems, similarity solutions and conservation laws of the Tzitzéica-Dodd-Bullogh equation

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New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

“…To assure the analytic solvability of NLPDEs, integrability is a crucial aspect. In recent years, the various applications of integrability and localized wave solutions of numerous NLPDEs can be noticed such as, the rogue wave and multiple lump solutions in the form of Grammian formula for the (2 + 1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation have been obtained by using polynomial function approach in [6]; multiple lump molecules and interaction solutions for the Kadomtsev-Petviashvili I equation are employed by utilizing non-homogeneous polynomial technique in [7]; lump chain solutions for the (2 + 1)dimensional BKP equation have been determined by using the τ-function in the form of Grammian formula in [8]; the soliton-cnoidal wave and lump-type solutions for (2 + 1)-dimensional KdV-mKdV equation are derived by utilizing Lie symmetry analysis and Bäcklund transformation approaches in [9]. The theoretical studies in nonlinear evolution equations have various applications in the diverse area of science and technology, such as: the electrohydrodynamics of a thin suspended liquid film model, which describes an incompressible fluid is examined by the perturbation technique in [10]; the granular model arising in the fluid dynamics has been solved by Painlevé analysis, Bäcklund transformation, Jacobi elliptic function, and tanh function methods in [11]; the magma equation arising in porous media is examined by the Cole-Hopf transformation method in [12]; the turbulent magnetohydrodynamic model in plasma turbulence has been solved using complex ansatz method in [13]; the compressible magnetohydrodynamic equations in cold plasma is examined by using the reductive perturbation method in [14].…”