scholarly journals Strongly nonlinear perturbation theory for solitary waves and bions

2019 ◽  
Vol 8 (1) ◽  
pp. 1-29
Author(s):  
John Boyd ◽  
Keyword(s):  
Perturbation Theory ◽  
Solitary Waves ◽  
Nonlinear Perturbation ◽  
Strongly Nonlinear

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

On a convergent nonlinear perturbation theory without small denominators or secular terms

1976 ◽  
Vol 17 (1) ◽  
pp. 121-140 ◽  
Author(s):  
Charles R. Eminhizer ◽  
Robert H. G. Helleman ◽  
Elliott W. Montroll
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Perturbation ◽  
Small Denominators ◽  
Secular Terms

Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability

1996 ◽  
Vol 76 (17) ◽  
pp. 3112-3115 ◽  
Author(s):  
Alexander L. Velikovich ◽  
Guy Dimonte
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Perturbation

scholarly journals EXISTENCE OF SOLITARY WAVES AND PERIODIC WAVES TO A PERTURBED GENERALIZED KDV EQUATION

2014 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Weifang Yan ◽  
Zhengrong Liu ◽  
Yong Liang
Keyword(s):  
Perturbation Theory ◽  
Solitary Waves ◽  
Wave Speed ◽  
Kdv Equation ◽  
Upper And Lower Bounds ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Periodic Waves ◽  
Regular Perturbation ◽  
Generalized Kdv Equation

In this paper, the existence of solitary waves and periodic waves to a perturbed generalized KdV equation is established by applying the geometric singular perturbation theory and the regular perturbation analysis for a Hamiltonian system. Moreover, upper and lower bounds of the limit wave speed are obtained. Some previous results are extended.

scholarly journals A note on strongly nonlinear parabolic variational inequalities

2017 ◽  
Vol 2 (2) ◽  
pp. 443-448 ◽  
Author(s):  
A. T. El-Dessouky
Keyword(s):  
Variational Inequalities ◽  
Weak Solutions ◽  
A Priori ◽  
Nonlinear Perturbation ◽  
Existence Of Weak Solutions ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
A Priori Bound ◽  
Derivatives Of ◽  
Quasilinear Parabolic

AbstractWe prove the existence of weak solutions of variational inequalities for general quasilinear parabolic operators of order m = 2 with strongly nonlinear perturbation term. The result is based on a priori bound for the time derivatives of the solutions.

Sign in / Sign up

Export Citation Format

Share Document