scholarly journals Numerical study of the KP equation for non-periodic waves

2012 ◽  
Vol 82 (7) ◽  
pp. 1185-1218 ◽  
Author(s):  
Chiu-Yen Kao ◽  
Yuji Kodama
Keyword(s):  
Numerical Study ◽  
Periodic Waves ◽  
Kp Equation

scholarly journals Phase dynamics of periodic waves leading to the Kadomtsev–Petviashvili equation in 3+1 dimensions

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150137 ◽  
Author(s):  
Daniel J. Ratliff ◽  
Thomas J. Bridges
Keyword(s):  
Phase Modulation ◽  
Space Dimension ◽  
Travelling Waves ◽  
Wave Action ◽  
Periodic Waves ◽  
Kp Equation ◽  
Modulation Equation ◽  
Phase Dynamics ◽  
Quantum Vortex ◽  
Petviashvili Equation

The Kadomstev–Petviashvili (KP) equation is a well-known modulation equation normally derived by starting with the trivial state and an appropriate dispersion relation. In this paper, it is shown that the KP equation is also the relevant modulation equation for bifurcation from periodic travelling waves when the wave action flux has a critical point. Moreover, the emergent KP equation arises in a universal form, with the coefficients determined by the components of the conservation of wave action. The theory is derived for a general class of partial differential equations generated by a Lagrangian using phase modulation. The theory extends to any space dimension and time, but the emphasis in the paper is on the case of 3+1. Motivated by light bullets and quantum vortex dynamics, the theory is illustrated by showing how defocusing NLS in 3+1 bifurcates to KP in 3+1 at criticality. The generalization to N >3 is also discussed.

scholarly journals On a class of initial value problems and solitons for the KP equation: A numerical study

Wave Motion ◽  
2017 ◽  
Vol 72 ◽  
pp. 201-227 ◽  
Author(s):  
T. McDowell ◽  
M. Osborne ◽  
S. Chakravarty ◽  
Y. Kodama
Keyword(s):  
Initial Value Problems ◽  
Numerical Study ◽  
Kp Equation ◽  
Initial Value

On the three-dimensional internal waves excited by topography in the flow of a stratified fluid

1994 ◽  
Vol 263 ◽  
pp. 293-318 ◽  
Author(s):  
Hideshi Hanazaki
Keyword(s):  
Internal Waves ◽  
Numerical Study ◽  
Mach Reflection ◽  
Three Dimensional ◽  
Stratified Fluid ◽  
Linear Wave ◽  
Kp Equation ◽  
Subcritical Flow ◽  
Boussinesq Fluid ◽  
Upstream Waves

A numerical study of the three-dimensional internal waves excited by topography in the flow of a stratified fluid is described. In the resonant flow of a nearly two-layer fluid, it is found that the time-development of the nonlinearly excited waves agrees qualitatively with the solution of the forced KP equation or the forced extended KP equation. In this case, the upstream-advancing solitary waves become asymptotically straight crested because of abnormal reflection at the sidewall similar to Mach reflection. The same phenomenon also occurs in the subcritical flow of a nearly two-layer fluid. However, in the subcritical flow of a linearly stratified Boussinesq fluid, the two-dimensionalization of the upstream waves can be interpreted as the separation of the lateral modes due to the differences in the group velocity of the linear wave, although this does not mean in general that the generation of upstream waves is describable by the linearized equation.

Numerical study of the low-frequency atomic dynamics in a Lennard-Jones glass

1998 ◽  
Vol 77 (2) ◽  
pp. 473-484 ◽  
Author(s):  
M. Sampoli, P. Benassi, R. Dell'Anna,
Keyword(s):  
Numerical Study ◽  
Low Frequency ◽  
Lennard Jones
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