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I. Introduction

Non-linear Wave Theory (NWT) effectively addresses physical phenomena that Linear Wave Theory (LWT) struggles to describe, such as mass transport and energy transfer between waves of varying frequencies. NWT significantly improves prediction accuracy, particularly in complex scenarios like steep ocean wave crests. This theory's focus on periodic waves lays the groundwork for future research on irregular waves. Key governing equations involve Bernoulli's principle and boundary conditions, providing a framework for effective wave analysis.

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I. Introduction

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  1. I. Introduction Purposes & Applications • Certain physical phenomena cannot be described using Linear Wave Theory (LWT), but can be described by Non-linear WaveTheory (NWT), such as mass transport, nonlinear energy transfer among waves of different frequencies, and bound waves. • The prediction based on LWT sometimes is not accuracy. By using NWT, the accuracy of predictions can be greatly improved, for example, the wave kinematics near steep ocean wave crests.

  2. Nonlinear Periodic Wave Train • NWT based on periodic waves lays a solid foundations for future studies of NWT for irregular waves. • Governing Equations and Boundary Conditions

  3. Governing equation and boundary conditions are: C(t) is Bernoulli constant, and chosen so that the still water is at z = 0. The Characteristics of a regular wave train are sketched in the figure below.

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