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Nonlinear Water Waves and Nonlinear Evolution Equations with Applications

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Encyclopedia of Complexity and Systems Science

True Laws of Nature cannot be linear.

Albert Einstein

… the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations … and therefore we can learn by comparing different nonlinear problems.

Werner Heisenberg

… as Sir Cyril Hinshelwood has observed… fluid dynamics were divided into hydraulic engineers who observed things that could not be explained and mathematicians who explained things that could not be observed.

James Lighthill

Introduction

Water waves are the most common observable phenomena in nature. The subject of water waves is most fascinating and highly mathematical and verified of all areas in the study of wave motions in the physical world. The mathematical as well as physical problems deal with water waves and their breaking on beaches, with flood waves in rivers, with ocean waves from storms, with ship waves on water, and with free oscillations of enclosed waters such as lakes and harbors. The study...

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Authors and Affiliations

  1. Department of Mathematics, University of Texas-Pan American, Edinburg, TX, 78539-2999, USA

    Lokenath Debnath

  2. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, 79968, USA

    Kanadpriya Basu

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  1. Lokenath Debnath
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  2. Kanadpriya Basu
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Correspondence to Lokenath Debnath .

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Debnath, L., Basu, K. (2014). Nonlinear Water Waves and Nonlinear Evolution Equations with Applications. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_609-1

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