In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript.

Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

Dynamic behavior of the (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation

In this paper, a new (3+1)-dimensional Hirota bilinear equation in fluids is investigated. The interaction solutions of lump and N-soliton (
 $$N>1$$
 ) are obtained. When $$N=2, 3, 4$$
 , new dynamical behavior is analyzed. The interaction of lump and periodic solutions is studied, including lump and 1-periodic solution and lump and 2-periodic solution. The interaction of lump, periodic and 1-soliton solutions is discussed. Finally, we obtain the multi-lump solutions, including 1-order, 2-order and 3-order lump solutions.

Study on dynamical behavior of multiple lump solutions and interaction between solitons and lump wave

Qualitative analysis of solutions for the p Laplacian hyperbolic equation with logarithmic nonlinearity

Lump solutions are one of the most common solutions for nonlinear evolution equations. This study aspires to investigate the generalized Hietarintatype equation. We auspiciously provide multiple M-lump waves. On the other hand, collision phenomena to multiple M-lump waves with soliton wave solutions are also provided. During the collision, the amplitude of the lump will change significantly over the processes, whereas the amplitude of the soliton will just minimally alter. As it is of paramount importance, we use suitable values of parameter to put out the physical features of the reported results through three dimensional and contour graphics. The results presented express physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes. Further, this study serves to enrich nonlinear dynamics and provide insight into how nonlinear waves propagate.

Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle

The behavior of specific dispersive waves in a new $$(3+1)$$
 -dimensional Hirota bilinear (3D-HB) equation is studied. A Backlund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painleve expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.

Majid Samavat

Papers

A New $$(3+1)$$ -dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions

A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex $$N$$-Kink Solitons