Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

2017 ◽  
Vol 132 (12) ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solitary Wave ◽  
Stratified Fluid ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Mathematical Methods ◽  
Wave Solutions ◽  
Dimensional Interaction

Bounds for surface solitary waves

1974 ◽  
Vol 76 (1) ◽  
pp. 345-358 ◽  
Author(s):  
G. Keady ◽  
W. G. Pritchard
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Boundary Value Problem ◽  
Froude Number ◽  
Solitary Waves ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Value Problem ◽  
Solitary Wave Solutions ◽  
Maximum Displacement ◽  
Wave Solutions

In these notes we give proofs of some properties of surface solitary waves. Assuming the existence of solitary-wave solutions to the nonlinear boundary-value problem (P) defined below, it is shown (i) that the wave is a wave of elevation alone, and (ii) that at large distances it is asymptotic to a uniform supercritical stream (i.e. the Froude number , where c is the speed of the stream, h is its depth, and g is the gravity constant).We also deduce a number of inequalities relating F2 to a/h, where a is the maximum displacement of the free surface from its value at infinity. In particular, it is shown for the wave of greatest height that 1·480 < F2 < 2.

scholarly journals Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhigang Yao ◽  
Huayong Xie ◽  
Hui Jie
Keyword(s):  
Solitary Wave ◽  
Rogue Wave ◽  
Kdv Equation ◽  
Auxiliary Function ◽  
Mixed Solution ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Trilinear Form ◽  
Wave Solutions

Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

Solitary wave solutions for variant two-dimensional Zakharov-Kuznetsov equation

2017 ◽  
Vol 11 ◽  
pp. 347-352
Author(s):  
Juan Carlos Hernandez R. ◽  
Martha Cecilia Moreno ◽  
German Preciado L.
Keyword(s):  
Solitary Wave ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Wave Solutions
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