Linear and nonlinear waves (original) (raw)

Selected Topics in Nonlinear Wave Mechanics

2002

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Solutions of a Few Nonlinear Wave Equations in Engineering Sciences

2014

This paper obtains the soliton and other solutions to a few nonlinear wave equations that arise on a daily basis to various engineering disciplines and other fields. The sine-cosine method is adopted to extract these solutions. The ansatz method is also implemented to obtain a singular soliton solution to Schrödinger-Hirota equation that is studied in electrical engineering in the context of nonlinear fiber optics. In this context, both Kerr law and power law nonlinearity are going to be addressed. There are several constraint conditions that will be listed in order for the solutions to exist.

Nonlinear Vibrations and the Wave Equation

SpringerBriefs in Mathematics

SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians.

Solition solutions of a few nonlinear wave equations in engineering sciences

This paper obtains the soliton and other solutions to a few nonlinear wave equations that arise on a daily basis to various engineering disciplines and other fields. The sine-cosine method is adopted to extract these solutions. The ansatz method is also implemented to obtain a singular soliton solution to Schrödinger-Hirota equation that is studied in electrical engineering in the context of nonlinear fiber optics. In this context, both Kerr law and power law nonlinearity are going to be addressed. There are several constraint conditions that will be listed in order for the solutions to exist.

Nonlinear waves and solitons in physical systems

Physica D: Nonlinear Phenomena, 1998

Advances in nonlinear science have been plentiful in recent years. In particular, interest in nonlinear wave propagation continues to grow, stimulated by new applications, such as ber optic communication systems, as well as the many classical unresolved issues of uid dynamics. What is arguably the turning point for the modern perspective of nonlinear systems took place at Los Alamos over forty years ago with the pioneering numerical simulations of Fermi, Pasta, and Ulam. A decade later, this research initiated the next major advance of Zabusky and Kruskal that motivaded the revolution in completely integrable systems. With this in mind, the conference on Nonlinear Waves in Solitons in Physical Systems (NWSPS) was organized by the Center for Nonlinear Studies (CNLS) at Los Alamos National Laboratory in May of 1997, to assess the current state-of-the-art in this very active eld. Papers from the conference attendees as well as from researchers unable to attend the conference were collected in this special volume of Physica D. In this paper, the contributions to the conference and to this special issue are reviewed, with an emphasis on the many unifying principles that all these works share. be broken into pieces, which are then solved independently by, for example, the Fourier or Laplace transform, and then added back to form a solution to the original problem.

Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics

2012

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinear wave equations from which they arise. We focus on a semilinear perturbation of Maxwell's equations and the nonlinear Klein-Gordon equation coupled with Maxwell's equations. Physical ramifications of these equations are also discussed.