# Solitons And Nonlinear Wave Equations Dodd Pdf Writer

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- A New Analytical Model for Internal Solitons in the Ocean
- Study of Functional Variable Method for Finding Exact Solutions of Nonlinear Evolution Equations
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- Nonlinear Processes in Physics

We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.

## A New Analytical Model for Internal Solitons in the Ocean

The interest in nonlinear physics has grown significantly over the last fifty years. Although numerous nonlinear processes had been previouslyidentified the mathematic tools of nonlinear physics had not yet been developed. The available tools were linear, and nonlinearities were avoided or treatedas perturbations of linear theories.

JohnScott Russell carried out many experiments to obtain the properties of this wave. The theories which were based on linear approaches concluded that thiskind of wave could not exist. The controversy was resolved by J. Skip to main content Skip to table of contents.

This service is more advanced with JavaScript available. Encyclopedia of Complexity and Systems Science Edition. Editors: Robert A. Meyers Editor-in-Chief. Contents Search. Solitons: Historical and Physical Introduction. How to cite. Definition of the Subject The interest in nonlinear physics has grown significantly over the last fifty years.

This is a preview of subscription content, log in to check access. Primary Literature 1. Airy GB Tides and waves. Encycl Metropolitana — Google Scholar. Part 1 Theory. MSE — Google Scholar. Bullough RK The Wave Par Excellence, the solitary progressive great wave ofequilibrium of the fluid: an early history of the solitary wave.

In: Lakshmanan M ed Solitons: Introduction and applications. Springer Ser Nonlinear Dyn. Springer, Berlin Google Scholar. Premiers constats. Houille Blanche —32 Google Scholar. Dias F, Dutykh D Dynamics of tsunami waves. Springer, Opatija, Croatia Google Scholar. Brisbane, Australia Google Scholar. John Murray, London Google Scholar. Los Alamosreport, LA University of Chicago Press Google Scholar.

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Comparisons with experiments. Normal dispersion. Hashizume Y Nonlinear pressure wave propagation in arteries. Helal MA Review: Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics. Hirota R Exact solution of the Korteweg—de Vries equation for multiplecollisions of solitons.

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In: Environmental stratified flows. RussellJS Report on the committee on waves. Russell JS Experimental researches into the laws of certain hydrodynamical phenomena that accompany the motion of floating bodies, andhave not previously been reduced into conformity with the known laws of the resistance of fluids.

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Academic Press, London Google Scholar. HasegawaA Optical Solitons in Fibers. Wiley, New York Google Scholar. TodaM Theory of Nonlinear Lattices.

## Study of Functional Variable Method for Finding Exact Solutions of Nonlinear Evolution Equations

The interest in nonlinear physics has grown significantly over the last fifty years. Although numerous nonlinear processes had been previouslyidentified the mathematic tools of nonlinear physics had not yet been developed. The available tools were linear, and nonlinearities were avoided or treatedas perturbations of linear theories. JohnScott Russell carried out many experiments to obtain the properties of this wave. The theories which were based on linear approaches concluded that thiskind of wave could not exist.

By considering the ansatz method, the authors successfully construct the bright and dark soliton solutions of the equation. The sub-equation method is also extended to find its complexitons solutions. Moreover, the explicit power series solution is also derived with its convergence analysis. Finally, the influences of each parameter on these solutions are discussed via graphical analysis. Authors express their sincere thanks to the editor and reviewers for their valuable comments. Tian, S. Report bugs here.

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Editors view affiliations A. Fokas D.

Recent Advances in Solution Methods for Nonlinear Evolution Equations, Fluid the Lax equation, the Sawada-Kortera (SK) equation, the Caudrey-Dodd-Gibbon and the SK equation are completely integrable and possess -soliton solution. We investigate the traveling wave solutions of the nonlinear wave equation (1).

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Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Editors view affiliations A. Fokas D.

Metrics details. This model describes the propagation of moving two-waves under the influence of dispersion, nonlinearity, and phase velocity factors. We seek possible stationary wave solutions to this new model by means of Kudryashov-expansion method and sine—cosine function method. Also, we provide a graphical analysis to show the effect of phase velocity on the motion of the obtained solutions. Stationary wave solutions for nonlinear equations play an important role in understanding many mathematical models arising in physics and applied sciences.

### Nonlinear Processes in Physics

The aim of this paper is to obtain the exact solutions of the strain wave equation applied for illustrating wave propagation in microstructured solids. The effective Kudryashov and functional variable methods along with the symbolic computation system have been used to accomplish the purpose. The search for the exact solutions of nonlinear partial differential quations PDEs has been one of the most important concerns of mathematicians throughout the world for a long time.

It is given to very few in science to be able to say, as could J. Scott Russell in , that one has discovered a wholly new natural phenomenon. Lord Russell's report on his observations of a solitary hydrodynamic wave in the windings of a Scottish barge canal is a splendid example of both such a discovery and of nineteenth-century scientific writing, and is well worth reading to this day Russell ,

A direct method, called the functional variable method, has been used to construct the exact solutions of nonlinear evolution equations NLEEs in mathematical physics. The obtained solutions contain an explicit function of the variables in the considered equations. It has been shown that the method provides a powerful mathematical tool for solving NLEEs in mathematical physics and engineering fields without the help of a computer algebra system. On the functional variable method for finding exact solutions to a class of wave equations. M Eslami and M Mirzazadeh. Functional variable method to study nonlinear evolution equations. The functional variable method and its applications for finding the exact solutions of nonlinear PDEs in mathematical physics.

Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions. Solitons as localized nonlinear waves exhibit many interesting properties [ 1 ]. In particular, solitons can form stable bound states known as soliton molecules, which have been observed experimentally in some fields [ 2 — 8 ].

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Request PDF | Exp-function method for nonlinear wave equations | In this paper, November ; Chaos Solitons & Fractals 30(3) The modified KdV equation and Dodd–Bullough–Mikhailov equation are chosen we will write the Van der Pol equation as the following forms: and we will give.

PDF | The extended tanh method is used to derive abundant solitary wave traveling and solitary wave solutions of nonlinear evolution equations have IJNS email for contribution: [email protected] [23] Wazwaz, A.M.:The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov.

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