Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation

Variable-coefficients nonlinear evolution equations offer us with more real aspects in the inhomogeneities of media and non-uniformities of boundaries than their counter constant-coefficients in some real-world problems. This study investigates the nonautonomous complex wave solutions to the (2 + 1)-dimensional variable-coefficients nonlinear Chiral Schrodinger equation (VCCE). The edge states of the fractional quantum hall effect is described by VCCE. We successfully reached the dark, bright, singular solitons and periodic wave solutions to this nonlinear model. To give more information about the physical features of the reported solutions, 3D and contour plots are successfully depicted in this paper.

Nonautonomous complex wave solutions to the (2+1)-dimensional variable-coefficients nonlinear Chiral Schrödinger equation

In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrodinger-Boussinesq system that includes beta derivative. The new exact solution is obtained have a hyperbolic function, trigonometric function, exponential function, and rational function. These solutions might appreciate in laser and plasma sciences. It is shown that this method, provides a straightforward and powerful mathematical tool for solving the nonlinear problems. Moreover, the linear stability of this nonlinear system is analyzed.

Dynamical behaviors to the coupled Schrödinger-Boussinesq system with the beta derivative

In this paper, the new 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations newly announced are investigated with the introduction of the spatial and sequential fractional-order derivatives expending in the sense of conformable derivative. Several solutions containing hyperbolic and trigonometric function solutions are created using the modified extended tanh-function (mETF) method. The productivity of the mETF process for building these solutions has been established. This method decreases the large volume of calculations. With the assist of computational software MALAB, the solutions' graphical exemplifications are illustrated in three-dimension (3D) and two-dimension (2D) plot. All plots represent the absolute wave configurations through the obtained solutions to the mentioned equation, preferring suitable parameters. Moreover, it may conclude that the attained solutions and their physical features might help comprehend the shallow water wave propagation in nonlinear dynamics.

Exact and explicit travelling-wave solutions to the family of new 3D fractional WBBM equations in mathematical physics

In this paper, the multivariate trilinear operators in the ($$3+1$$)-dimensional space are applied to a ($$3+1$$)-dimensional GBK equation. The resulting trilinear form is used to study its wave dynamics. Particularly, we generate a type of new interaction solutions between breather lump-type solitons and other multi-kink solitons, thereby formulating a kind of breather lump–kink solitons. By setting time constants, we change the coordinates of kink solitons to make them collide with the breather lump-type soliton, during which breather lump-type soliton is swallowed eventually by those kink solitons. The evolution behaviours of the breather lump–kink solitons are depicted by plotting 3-D and density graphs from the perspective of wave characteristics.

Lump-type solution and breather lump–kink interaction phenomena to a ( $$\mathbf{{3{\varvec{+}}1}}$$3+1 )-dimensional GBK equation based on trilinear form

We consider the simplified (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. We use the binary Bell polynomial theory to construct a bilinear form of the equation, and then construct a bilinear form of the special case of $$z = x$$
 . In the reduced bilinear form, we constructed a more general lump solution that is positioned in any direction of the space to have more arbitrary autocephalous parameters. The lump solution can produce striped solitons, which provides a lumpoff solution. Combined with the strip solitons, we can know that when the double solitons cut the lump solution, we obtain a special rogue waves. It can be seen from our research results that the time and place of the rogue wave can be captured by tracking the moving path of the lump solution.

Bilinear formalism, lump solution, lumpoff and instanton/rogue wave solution of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

In this work, we consider the chiral nonlinear Schrodinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries.

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Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions

The purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional variable-coefficient generalized B-type Kadomtsev–Petviashvili (vcgBKP) equation as examples.,Based on Hirota’s bilinear theory, a direct method is used to examine the lump solutions of these two equations.,The complete non-elastic interaction solutions between a lump and a stripe are also discussed for the equations, which show that the lump solitons are swallowed by the stripe solitons.,The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional KP-type nonlinear wave equations.

Xing-Jie Yan

Papers

Bilinear formalism, lump solution, lumpoff and instanton/rogue wave solution of a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

Modulation instability analysis of the generalized nonlinear Schrödinger equation and its bright, dark and complexiton soliton solutions