Solitary Wave Ansatz Research Articles

Explicit bright and dark solitons for the variable coefficient Biswas–Milovic equation with competing nonlinearity

This paper is devoted in the study of Biswas–Milovic equation with variable coefficients associated with four different forms of nonlinearity, namely the Kerr law, power law, parabolic law and the dual-power law. We prove that, in presence of additional time dependent damping term, yet there exists different solitary wave solutions under some constraint relations. The generalized form of solitary wave ansatz method in context of doubly periodic Jacobi elliptic functions is carried out to obtain bright and dark soliton solutions of the governing equation. The constraint relations between the model coefficients and the damping coefficient for existence of soliton solutions are derived. In addition, it is shown that for the existence of soliton, the damping coefficient has to be Riemann integrable. The remarkable features of such solitons are demonstrated in several interesting figures.

Soliton solutions of nonlinear wave equation in finite de-formation elastic cylindrical rod by solitary wave ansatz method

<p>In this paper, we consider nonlinear wave equation in finite deformation elastic cylindrical rod and obtain soliton solutions by Solitary Wave Ansatz method. It is shown that the ansatz method provides a very effective and powerful mathematical tool for obtaining solutions for Nonlinear Evolution Equations (NLEEs) in nonlinear Science.</p><div style="mso-element: para-border-div; border: none; border-bottom: solid windowtext 1.0pt; mso-border-bottom-alt: solid windowtext .25pt; padding: 0cm 0cm 1.0pt 0cm;"><p class="IJOPCMKeywards" style="margin-bottom: 0.0001pt; text-align: justify; border: none; padding: 0cm;"><span style="font-size: 8.0pt; mso-fareast-language: EN-US;">Elastic Rod; Finite Deformation; Nonlinear Wave Equation; Solitary Wave Ansatz Method; Soliton.</span></p></div>

Soliton and periodic solutions for time-dependent coefficient non-linear equation

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev–Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of functions and the modified sine–cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients

In this article, the solitary wave and topological soliton solutions in the models that describe the propagation of surface water waves in a uniform channel are successfully constructed. The solitary wave ansatz is used to carry out these distinct solutions. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

Optical soliton solutions for the variable coefficient modified Kawahara equation

In this paper, we obtain the 1-soliton solutions of the variable-coefficient modified Kawahara equation (VCMKE). The dark optical as well as bright optical soliton solutions were found related to the model considered in this study. The solitary wave ansatz method is used to carry out the integration.

Bright, dark, and singular solitons in magneto-electro-elastic circular rod

In this article, the bright, dark, and singular solitons are being constructed for nonlinear longitudinal wave equation with dispersion caused by transverse Poisson’s effect in a magneto-electro-elastic circular rod. The solitary wave ansatz is used to carry out these solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. This article provides a lot of encouragement for the researchers in this era.

Analytical and soliton solutions: Nonlinear model of nanobioelectronics transmission lines

In this article, analytical solutions and different types of soliton envelopes: bright, dark and singular for the nonlinear model, namely, nanobioelectronics transmission lines have been constructed along with constrained conditions. The modified extended tanh-function method and exp-function method have been used to find analytical solutions, and while solitary wave ansatz is used to construct these soliton solutions. Additionally, the constraint conditions, for the existence of the soliton solutions are also listed.

Conservation Laws and Soliton Solutions of the (1+1)-Dimensional Modified Improved Boussinesq Equation

AbstractIn this work, we consider the (1+1)-dimensional modified improved Boussinesq (IMBq) equation. As the considered equation is of evolution type, no recourse to a Lagrangian formulation is made. However, we showed that by utilising the partial Lagrangian method and multiplier method, one can construct a number of local and nonlocal conservation laws for the IMBq equation. In addition, by using a solitary wave ansatz method, we obtained exact bright soliton solutions for this equation. The parameters of the soliton envelope (amplitude, widths, velocity) were obtained as function of the dependent model coefficients. Note that, it is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.

Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations

AbstractIn this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existence of the solitons are identified during the derivation of the solution. Since, the nonlinear wave is one of the fundamental object of nature and a growing interest has been given to the propagation of nonlinear wave in dynamical system.

Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules

In this letter, the solitary wave and shock wave solitons for nonlinear equation of special interest in nanobiosciences, namely the transmission line model for nano-ionic currents along microtubules, have been constructed successfully. The solitary wave ansatz is used to carry out the solutions which shows the consistency.

BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

New Applications to Solitary Wave Ansatz

In this article, the solitary wave and shock wave solitons for nonlinear Ostrovsky equation and Potential Kadomstev-Petviashvili equations have been obtained. The solitary wave ansatz is used to carry out the solutions.

Topological (dark) soliton solutions for the Camassa–Holm type equations

In this paper, the topological (dark) soliton solutions to the Camassa–Holm type equations are obtained by the solitary wave ansatz method. This solution may be useful to explain some physical phenomena in genuinely nonlinear dynamical systems that are described by Camassa–Holm type models.

Topological soliton solutions for some nonlinear evolution equations

In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc.) envelope for the understanding of most nonlinear physical phenomena.

Bright and dark soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation and generalized Benjamin equation

In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sechp and \(\tanh^{p}\) functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.

Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with self-steepening and self-frequency shift effects

In this paper, we have obtained the optical solitary wave solutions for the nonlinear Schrödinger equation which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method was used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses were determined. Using the 1-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa-Satsuma cases. We have also constructed some periodic wave solutions of the higher order nonlinear Schrödinger equation by reducing it to quartic anharmonic oscillator equation and by using projective Ricatti equations. Moreover by using He's semi-inverse method, variational formulation was established to obtain exact soliton solutions. The 1-soliton solutions of time dependent form of this equation was also obtained. To visualize the propagation characteristics of dark-bright soliton solutions, few numerical simulations are given.

1-Soliton solutions of complex modified KdV equation with time-dependent coefficients

In this paper, we have obtained exact 1-soliton solutions of complex modified KdV equation with variable—coefficients using solitary wave ansatz. Restrictions on parameters of the soliton have been observed in course of the derivation of soliton solutions. Finally, a few numerical simulations of dark and bright solitons have been given.

DARK AND BRIGHT SOLITARY WAVE SOLUTIONS OF THE HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION WITH SELF-STEEPENING AND SELF-FREQUENCY SHIFT EFFECTS

In this paper, we obtain the exact bright and dark soliton solutions for the nonlinear Schrödinger equation (NLSE) which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method is used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses are determined. Using the one-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa–Satsuma cases and finally, we have constructed some periodic wave solutions by reducing the higher order nonlinear Schrödinger equation (HNLS) to quartic anharmonic oscillator equation. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a HNLS model equation.

Soliton solutions of some nonlinear evolution equations with time-dependent coefficients

In this paper, we obtain exact soliton solutions of the modified KdV equation, inhomogeneous nonlinear Schrodinger equation and G(m, n) equation with variable-coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.

Soliton-like solutions to the generalized Burgers-Huxley equation with variable coefficients

AbstractIn this paper, we consider the generalized Burgers-Huxley equation with arbitrary power of nonlinearity and timedependent coefficients. We analyze the traveling wave problem and explicitly find new soliton-like solutions for this extended equation by using the ansatz of Zhao et al. [X. Zhao, D. Tang, L. Wang, Phys. Lett. A 346 (2005) 288–291]. We also employ the solitary wave ansatz method to derive the exact bright and dark soliton solutions for the considered evolution equation. The physical parameters in the soliton solutions are obtained as function of the time-dependent model coefficients. The conditions of existence of solitons are presented. As a result, rich exact travelling wave solutions, which contain new soliton-like solutions, bell-shaped solitons and kink-shaped solitons for the generalized Burgers-Huxley equation with time-dependent coefficients, are obtained. The methods employed here can also be used to solve a large class of nonlinear evolution equations with variable coefficients.