N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

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

Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed KdV equation using Hirota-bilinear approach

In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma. The Nth-order Wronskian solutions for that equation are derived and proved under certain variable-coefficient constraints, where N is a positive integer. One-, two- and three-soliton solutions in the Wronskian for that equation are given. By means of the Pfaffianization procedure, a coupled (3+1)-dimensional GVCKP system is constructed from that equation. Bilinear form for that coupled system is exported. Under certain variable-coefficient constraints, those Wronski-type and Gramm-type Pfaffian solutions for that coupled system are obtained and proved with the help of the Pfaffian identities.

Wronskian solutions and Pfaffianization for a(3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma

Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics

In present work, we formulate a new generalized nonlinear KdV-type equation of fifth-order using the recursion operator. This equation generalizes the Sawada-Kotera equation and the Lax equation that study the vibrations in mechanical engineering, nonlinear waves in shallow water, and other sciences. To determine the integrability, we use Painlevé analysis and construct solutions for multiple solitons by employing the Hirota bilinear technique to the established equation. It produces a bilinear form for the driven equation and utilizes the Lagrange interpolation to create a dependent variable transformation. We construct the solutions for multiple solitons and show the graphics for these built solutions. The mathematical software program Mathematica employs symbolic computation to obtain the multiple solitons and various dynamical behavior of the solutions for newly generated equation The Sawada-Kotera equation and Lax equation have various applications in mechanical engineering, plasma physics, nonlinear water waves, soliton theory, mathematical physics, and other nonlinear fields.

A generalized nonlinear fifth-order KdV-type equation with multiple soliton solutions: Painlevé analysis and Hirota Bilinear technique

In this paper, we introduce two dimensional difference operator and its inverse by which we obtain two dimensional Fibonacci sequence and its sum. Some theorems and interesting results on the sum of the terms of two dimensional Fibonacci sequence are derived. Suitable examples are provided to illustrate our results.

https://scindeks-clanci.ceon.rs/data/pdf/2217-5539/2016/2217-55391602131X.pdf

Sum of two dimensional Fibonacci sequence by solutions of second order difference equations

A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas

B. Mohan

Papers

Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics

A generalized nonlinear fifth-order KdV-type equation with multiple soliton solutions: Painlevé analysis and Hirota Bilinear technique

Sum of two dimensional Fibonacci sequence by solutions of second order difference equations

A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas