A study of multi-soliton solutions, breather, lumps, and their interactions for kadomtsev-petviashvili equation with variable time coeffcient using hirota method

Bilinear form and Pfaffian solutions for a (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics and plasma physics

Rogue-wave, rational and semi-rational solutions for a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer fluid

Nonlinear superposition between lump and other waves of the (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid dynamics

Hybrid localized wave solutions for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

Variable-coefficient nonlinear evolution equations offer us with more real aspects in the inhomogeneities of media and non-uniformities of boundaries than their constant coefficients in some real-world problems. A $$(3+1)$$
 -dimensional variable coefficient Date–Jimbo–Kashiwara–Miwa (vcDJKM) equation and a $$(3+1)$$
 -dimensional variable coefficient Boiti–Leon–Manna–Pempinelli (vcBLMP) equation are studied based on the homoclinic test method and construction of abundant solutions for two kinds of equations are obtained with the help of symbolic computation. In order to study the interaction superposition solutions with different functions, an existence theorem and corollary about superposition solutions of the $$(3+1)$$
 -dimensional vcBLMP equation are proved. Via three-dimensional profiles with the help of mathematics, the propagation and the dynamical behavior of these solutions are analyzed by choosing different arbitrary variable coefficients. Compare with the published studied, some completely new results are presented in this paper.

Construction of abundant solutions for two kinds of $$\mathbf {(3\varvec{+}1)}$$-dimensional equations with time-dependent coefficients

Water wave is one of the most common phenomena in nature, and its involves mathematical modeling, aerodynamics, computer simulation, mechanical manufacturing, marine science and so on. Hence, the water wave dynamics of a (
 $$4+1$$
 )-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid is investigated based on the Hirota bilinear method and homoclinic test method. We are aimed at constructing variable coefficient solutions to the equation under consideration. An existence theorem and corollary about superposition solutions of this equation are proved. The water wave dynamic behaviors of the reported results are presented by a careful choice of the arguments for the trigonometric and hyperbolic functions as the values of the variable coefficients. With the help of Mathematica, the effect of the variable coefficients on the reported results can be clearly seen by the three-dimensional profiles. Compared with the published studied, some completely new mathematical results and physical phenomena are presented in this paper. The results are beneficial to the study of water waves in fluid dynamics, and this technique has opened a new way to explain the physical properties of nonlinear phenomena.

Interaction of multiple superposition solutions for the $$(4 + 1)$$ ( 4 + 1 ) -dimensional Boiti-LeonManna-Pempinelli equation

In this article, the bilinear form, Backlund transformation, Lax pair and infinite conservation laws of the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients are constructed based on the Bell polynomials approach. N-soliton solutions are studied by means of introducing the complex conjugate condition technique and selecting appropriate test functions and parameters, including the hybrid solution of the a-order kink waves, b-order periodic-kink waves and c-order periodic-breather waves. The homoclinic test method is applied to investigate their dynamical interaction properties between different forms of hybrid-type solutions. Besides, a number of examples are presented by choosing different types of interactions among the hybrid-type solutions. Finally, we analyze the wave propagation direction and velocity to reflect the novel evolutionary behaviors in the three-dimensional profile of the model. These results are helpful to the study of local wave interactions in nonlinear mathematical physics.

Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients

Higher-order mixed localized wave solutions and bilinear auto-Bäcklund transformations for the (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation

Taogetusang Bao

Papers

Construction of abundant solutions for two kinds of $$\mathbf {(3\varvec{+}1)}$$-dimensional equations with time-dependent coefficients

Hybrid localized wave solutions for a generalized Calogero–Bogoyavlenskii–Konopelchenko–Schiff system in a fluid or plasma

Interaction of multiple superposition solutions for the $$(4 + 1)$$ ( 4 + 1 ) -dimensional Boiti-LeonManna-Pempinelli equation

Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients

Higher-order mixed localized wave solutions and bilinear auto-Bäcklund transformations for the (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation