Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

El‐Ganaini, Shoukry; Kumar, Sachin; Niwas, Monika

doi:10.1016/j.joes.2022.01.006

Cited by 13 publications

(4 citation statements)

References 39 publications

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“…where μ ≠ − 1. If we expand the factorization given in equation (11) we get the following non linear second order differential equation 12) is a particular form of the mixed Liénard type equation with quadratic and linear terms Note that equation (12) reduces to the standard Liénard type equation when μ → 0. By comparing (2) and ( 12), one obtains the conditions for the parametric factorization over the functions j 1 and j 2 :…”

Section: Parametric Factorizationmentioning

confidence: 99%

“…In applications one often encounters differential equations in which both linear and quadratic terms are present. The importance of studying equation (2) is due tot the fact that this equation frequently appears as a mathematical model in physics, such as in the study of nonlinear convection-diffusion-reaction equations [11,12], in the Rayleigh-Plesset equation [13], in the Friedman-Lemaitre-Robertson-Walker cosmological equation [14], etc. Furthermore, equation (2) belongs to the type of second order Gambier equation when the coefficients are assumed to be constant parameters.…”

Section: Introductionmentioning

confidence: 99%

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Parametric factorization of non linear second order differential equations

González Contreras

2024

Phys. Scr.

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Section: Parametric Factorizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric factorization of non linear second order differential equations

González Contreras

2024

Phys. Scr.

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“…On substituting the equations (21), (22) By puttting the equations ( 25), ( 29) and (30) into the equation ( 16), we determine a solution for two solitons for the equation (6).…”

Section: One Solitonmentioning

confidence: 99%

“…Many techniques other than the Hirota bilinear method construct the exact or closed-form solutions of a nonlinear PDE. These include the Inverse scattering method [15,16], Equivalence transformation [17], Velocity resonance method [18], Lie symmetry analysis [19][20][21][22], simplified Hirota method [23,24], Bilinear residual network method [25,26], Darboux transformation [27,28], Bäcklund transformation [29,30], and others [31,32].…”

Section: Introductionmentioning

confidence: 99%

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

Kumar¹,

Mohan²

2022

Phys. Scr.

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In this 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 behaviors of the newly generated solutions. 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.

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Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Ali

2024

Z. Angew. Math. Phys.

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In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light propagation in nonlinear optical fibers or photonic crystals where the refractive index has a q-deformed structure; and it also can be applied in studying shock waves, turbulence and rogue waves where the deformation introduces corrections to classical wave phenomena. Utilizing the $$(\frac{{\mathfrak {G}}^{\prime }}{\omega {\mathfrak {G}}^{\prime }+{\mathfrak {G}}+r})$$ ( G ′ ω G ′ + G + r ) -expansion technique, we derive novel analytical solutions that enhance our understanding of the underlying dynamics. Additionally, we employ a finite element method (extended cubic B-spline method) to validate our analytical findings and explore the behavior of the q-deformed equation under different parameter regimes. Our results demonstrate the versatility of the q-deformed framework in generating rich optical phenomena, paving the way for future research in both theoretical and applied physics.

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Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

Cited by 13 publications

References 39 publications

Parametric factorization of non linear second order differential equations

Parametric factorization of non linear second order differential equations

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

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

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