Cnoidal wave solutions for the optical Benney-Luke equation

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

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Solitary wave solutions and cnoidal wave solutions to the combined KdV and mKdV equation

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.1670170503 ◽

1994 ◽

Vol 17 (5) ◽

pp. 339-347 ◽

Cited By ~ 13

Author(s):

Sen-Yue Lou ◽

Li-Li Chen

Keyword(s):

Solitary Wave ◽

Mkdv Equation ◽

Cnoidal Wave ◽

Solitary Wave Solutions ◽

Wave Solutions

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A Nonlinear Shallow Water Theory and Its Application to Cnoidal Wave Solutions and Mass Transport

Journal of the Physical Society of Japan ◽

10.1143/jpsj.51.4108 ◽

1982 ◽

Vol 51 (12) ◽

pp. 4108-4115 ◽

Cited By ~ 1

Author(s):

Kimiaki Konno ◽

Alan Jeffrey

Keyword(s):

Mass Transport ◽

Shallow Water ◽

Cnoidal Wave ◽

Shallow Water Theory ◽

Wave Solutions ◽

Nonlinear Shallow Water Theory

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A high-order cnoidal wave theory

Journal of Fluid Mechanics ◽

10.1017/s0022112079000975 ◽

1979 ◽

Vol 94 (1) ◽

pp. 129-161 ◽

Cited By ~ 64

Author(s):

J. D. Fenton

Keyword(s):

Shallow Water ◽

Wave Height ◽

Water Depth ◽

Wave Theory ◽

High Order ◽

Stokes Wave ◽

Cnoidal Wave ◽

Expansion Parameter ◽

Wave Solutions ◽

Fifth Order

A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested.Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results.

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