Traveling Wave Hypothesis Research Articles

Soliton perturbation and conservation laws in magneto-optic waveguides with parabolic law nonlinearity

This paper secures bright and singular perturbed optical solitons in magneto-optic waveguides, having parabolic form of nonlinearity, with traveling wave hypothesis. The conservation laws are subsequently obtained by the multiplier approach and the three conserved quantities are finally listed.

Optical wave structures to the Fokas–Lenells equation

The Fokas–Lenells (FL) equation that describes the soliton dynamics precisely in waveguides is investigated in the present paper. The planned goal is performed by utilizing a traveling wave hypothesis for reducing the FL equation and handling the resulting ODE using the expa and Jacobi elliptic function methods. As an outcome, optical wave structures of the FL equation with useful information are acquired successfully.

Optical dromions, domain walls and conservation laws with Kundu–Mukherjee–Naskar equation via traveling waves and Lie symmetry

This paper secures optical dromions, domain walls and conservation laws for Kundu–Mukherjee–Naskar equation. Three integration approaches are applied. These are traveling wave hypothesis, method of undetermined coefficients and Lie symmetry. Finally, multiplier approach yielded two conservation laws supported by the model. These are power and Hamiltonian that are expressed in quadratures.

Bright and singular optical solitons for Kaup–Newell equation with two fundamental integration norms

This paper retrieves soliton solutions to Kaup–Newell's equation in optical fibers. Two fundamental integration schemes, namely the csch-function method and traveling wave hypothesis, obtain singular and bright soliton solutions respectively. The existence criteria for these solitons are also presented.

Numerical Studying of Soliton in the Korteweg-de Vries (KdV) Equation

In this paper, we use a numerical approach for finding soliton of the Korteweg-de Vries (KdV) equation in infinite dimensionalization. The traveling wave hypothesis is used to extract the analytic soliton solution of KdV equation. Barbera (1993) shown that KdV equation is a solution of Hamiltonian energy optimization in the level set of the momentum. We numerically solve the optimization problem by using steepest descent method and adding the assumption to guarantee the constraint will be fulfilled. From this method, the dynamic system of the problem is obtained and finite difference implementation is used for solving the dynamic system. Based on the method and the hypothesis, the soliton is obtained.

Chirp-free bright optical solitons and conservation laws for complex Ginzburg-Landau equation with three nonlinear forms

This paper obtains chirp-free bright optical soliton solutions to the complex Ginzburg-Landau equation by traveling wave hypothesis and semi-inverse variational principle. Three forms of nonlinearity are associated with the model. They are quadratic-cubic form, parabolic law and dual-power law. The corresponding conservation laws are also included.

Chirp-free bright optical soliton perturbation with Chen–Lee–Liu equation by traveling wave hypothesis and semi-inverse variational principle

Chirp-free bright optical soliton solutions are obtained for Chen–Lee–Liu equation by traveling wave hypothesis as well as the application of semi-inverse variational principle. The constraint conditions for the existence of these solitons are also presented.

Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis

This paper obtains chirp-free bright optical soliton solutions to Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis along with the technical criteria for the existence of such solitons. The speed of the soliton also emerges from the constraint condition.

Chirp-free bright optical soliton perturbation with Fokas–Lenells equation by traveling wave hypothesis and semi-inverse variational principle

This paper secures chirp-free bright optical solitons to perturbed Fokas–Lenells equation. Two integration algorithms are applied. They are traveling wave hypothesis and the semi-inverse variational principle. The parameter restrictions for the existence of solitons are also presented.

Optical soliton perturbation of Fokas–Lenells equation with two integration schemes

This paper obtained singular and dark-singular combo solitons to Fokas–Lenells equation by the aid of traveling wave hypothesis. The modified simple equation scheme retrieved plane wave solutions to the model. The existence criteria of these waves are also presented.

Decomposition method using He s polynomials for Kdv Boussinesq and coupled Kdv Boussinesq equations

This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He’s polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations.

Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas

In this paper, we extended the improved \(\tan(\phi/2)\)-expansion method (ITEM) and the generalized \(G'/G\)-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved \(\tan(\phi/2)\)-expansion method, the generalized \(G'/G\)-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, \(G'/G\)-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.

Analytical study of solitons for the variant Boussinesq equations

In this paper, two useful methods that are traveling wave hypothesis and auxiliary function method are constructed new periodic solution, kink soliton solution and bell-shaped solitary wave solution of the variant Boussinesq equations. The existence conditions are given. A pair of solitary wave solutions via the traveling wave hypothesis is mainly studied: the waveform change and the nature of the analysis depending on the choice of solitonic parameters. A new physical phenomenon occurring in this system is the waveform of each soliton gets change or recovery under different parameters, which might provide us with a different approach of load information transfer.

Optical solitons and conservation laws with anti-cubic nonlinearity

This paper obtains bright, dark and singular 1-soliton solution to nonlinear Schrödinger's equation that is studied with anti-cubic nonlinearity for optical fibers. The traveling wave hypothesis leads to implicit solution in terms of elliptic functions. The method of undetermined coefficients yields explicit single soliton solutions. Finally, a comprehensive discussion on conservation laws closes the chapter.

Raman solitons in nanoscale optical waveguides, with metamaterials, having polynomial law non-linearity

This paper reports bright Raman soliton solutions in optical metamaterials. The polynomial law and triple law non-linearity are discussed. Travelling wave hypothesis is employed to conduct the mathematical analysis. Implicit solutions in terms of elliptic integral of the third kind are obtained. The analytical results are supplemented with numerical simulations.

Exact traveling wave solutions for system of nonlinear evolution equations.

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Analytical study of solitons in magneto-electro-elastic circular rod

The nonlinear longitudinal wave equation, describing the propagation of optical solitons in magneto-electro-elastic circular rod, is investigated analytically. Two integration tools that are traveling wave hypothesis and G\(^{\prime }\)/G expansion scheme are recruited to extract explicit soliton solutions. The existence conditions are derived.

Analytical study of Thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

This paper presents for the first time an analytic study on Thirring optical solitons in birefringent fibers with parabolic law nonlinearity and spatio-temporal dispersion. The dynamical model for the propagation of Thirring optical solitons is given by the vector coupled nonlinear Schrodinger equation, which is investigated analytically using two different ways. These algorithms, that are the traveling wave hypothesis and the P6 model scheme are employed to obtain bright, dark as well as singular solitons. The integrability conditions are also exhibited.

Solitons and other solutions of the long-short wave equation

Purpose– The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method,G′/G-expansion method and several others.Design/methodology/approach– The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results.Findings– The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions.Originality/value– The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation

This paper obtains soliton and other solutions to the Gardner-Kadomtsev-Petviashvili equation that models shallow water wave equation in (1+2)-dimensions. There are three types of integration architectures that will be employed in order to obtain several forms of solution to this model. These are traveling wave hypothesis, improved $G^{\prime}/G$-expansion method and finally the tanh-coth hypothesis. The constraint conditions that are needed, for these solutions to exist, are also reported.