Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation
نویسندگان
چکیده
منابع مشابه
Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation
We consider the solitary wave solutions of a Korteweg-de Vries equation, where the coefficients in the equation vary with time over a certain region. When these coefficients vary rapidly compared with the solitary wave, then it is well-known that the solitary wave may fission into two or more solitary waves. On the other hand, when these coefficients vary slowly, the solitary wave deforms adiab...
متن کاملWeakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly nonlinear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg–de Vries (KdV) equation. A progressive wave type of solution, which sati...
متن کاملChange of polarity for periodic waves in the variable-coefficient Korteweg-de Vries equation
We examine the variable-coefficient Kortweg-de Vries equation for the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the origin...
متن کاملSolitary waves of a coupled Korteweg-de Vries system
In the long-wave, weakly nonlinear limit a generic model for the interaction of two waves with nearly coincident linear phase speeds is a pair of coupled Korteweg-de Vries equations. Here we consider the simplest case when the coupling occurs only through linear non-dispersive terms, and for this case delineate the various families of solitary waves that can be expected. Generically, we demonst...
متن کاملDynamics of Solitary-waves in the Higher Order Korteweg – De Vries Equation Type (I)
We find new analytic solitary-wave solutions of the higher order wave equations of Korteweg – De Vries (KdV) type (I), using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves are stable for wide ranges of the model coefficients. We study the dynamics of the two solitary-waves by using the analytic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2004
ISSN: 0022-2526,1467-9590
DOI: 10.1111/j.0022-2526.2004.01521.x