ArticleScientific reports2025
Bifurcation analysis, modulation instability and dynamical analysis of soliton solutions for generalized (3 + 1)-dimensional nonlinear wave equation with m-fractional operator.
Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Analytical construction of needle-type solitons in a M-fractional paraxial wave framework with dynamical analysis.Scientific reports · 2026Article
- On certain novel numerical and analytical solutions for the pure-cubic Schrödinger equation in optical fibers with Kerr nonlinearity.Scientific reports · 2026Article
- Exploring complex phenomena in fluid flow and plasma physics via the Schrödinger-type Maccari system.Scientific reports · 2025Article
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6 authors.
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Abstract
This research investigates the bifurcation theory of a generalized (3 + 1)-dimensional P-type nonlinear wave equation with an M-fractional derivative (M-fGP-NWE) and develops its soliton solutions. The model is initially transformed into an ordinary differential equation form using a wave variable. By employing a Galilean transformation, a dynamical system of equations is obtained. The phase portrait and Hamiltonian function are examined under different parametric conditions, facilitating the identification of homoclinic and heteroclinic orbits. These orbits illustrate solitary, bell-shaped, periodic wave solutions for certain parameter values. The modified simple equation (MSE) method is employed to derive soliton solutions for the M-fractional generalized (3 + 1)-dimensional P-type nonlinear wave equation. The resultant solutions are articulated in hyperbolic, trigonometric, and exponential forms under parametric circumstances. Complex wave phenomena are further exemplified through detailed 3D, 2D, and density graphs for certain parameter values. Additionally, we also analyse the modulation Instability of the proposed model. The computational results and visual depictions validate the efficiency and dependability of the MSE method, highlighting its efficacy as a flexible solution for complex fractional differential equations.
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