ArticleHeliyon2024
Effect of the nonlinear dispersive coefficient on time-dependent variable coefficient soliton solutions of the Kolmogorov-Petrovsky-Piskunov model arising in biological and chemical science.
Article in Heliyon, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Unveiling solitary and twinning kink solitons in (2+1)-dimensional modified Zakharov-Kuznetsov equation arising in electronics.Scientific reports · 2025Article
- Bifurcation analysis, modulation instability and dynamical analysis of soliton solutions for generalized (3 + 1)-dimensional nonlinear wave equation with m-fractional operator.Scientific reports · 2025Article
- Bifurcation analysis and dynamical behavior of novel optical soliton solution of chiral (2 + 1) dimensional nonlinear Schrodinger equation in telecommunication system.Scientific reports · 2025Article
- Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity.Scientific reports · 2025Article
- Exploring novel solitary wave phenomena in Klein-Gordon equation usingScientific reports · 2025Article
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3 authors.
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Abstract
In this article, we study the soliton solutions with a time-dependent variable coefficient to the Kolmogorov-Petrovsky-Piskunov (KPP) model. At first, this model was used as the genetics model for the spread of an advantageous gene through a population, but it has also been used as a number of physics, biological, and chemical models. The enhanced modified simple equation technique applies to get the time-dependent variable coefficient soliton solutions from the KPP model. The obtained solutions provide diverse, exact solutions for the different functions of the time-dependent variable coefficient. For the special value of the constants, we get the kink, anti-kink shape, the interaction of kink, anti-kink, and singularities, the interaction of instanton and kink shape, instanton shape, kink, and bell interaction, anti-kink and bell interaction, kink and singular solitons, anti-kink and singular solitons, the interaction of kink and singular, and the interaction of anti-kink and singular solutions to diverse nature wave functions as time-dependent variable coefficients. The presented phenomena are clarified in three-dimension, contour, and two-dimension plots. The obtained wave patterns are powerfully exaggerated by the variable coefficient wave transformation and connected variable parameters. The effect of second-order and third-order nonlinear dispersive coefficients is also explored in 2D plots.
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