scholarly journals Random exponential attractor for stochastic discrete long wave-short wave resonance equation with multiplicative white noise

2020 ◽  
Vol 25 (8) ◽  
pp. 3153-3170
Author(s):  
Xingni Tan ◽  
◽  
Fuqi Yin ◽  
Guihong Fan ◽  
◽  
...  
Keyword(s):  
White Noise ◽  
Short Wave ◽  
Exponential Attractor ◽  
Long Wave ◽  
Wave Resonance ◽  
Multiplicative White Noise ◽  
Resonance Equation

Modeling internal rogue waves in a long wave-short wave resonance framework

2018 ◽  
Vol 3 (12) ◽  
Author(s):  
H. N. Chan ◽  
R. H. J. Grimshaw ◽  
K. W. Chow
Keyword(s):  
Rogue Waves ◽  
Short Wave ◽  
Long Wave ◽  
Wave Resonance

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

scholarly journals Dynamics of solitons in multicomponent long wave–short wave resonance interaction system

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 327-338 ◽  
Author(s):  
T KANNA ◽  
K SAKKARAVARTHI ◽  
M VIJAYAJAYANTHI ◽  
M LAKSHMANAN
Keyword(s):  
Short Wave ◽  
Resonance Interaction ◽  
Long Wave ◽  
Interaction System ◽  
Wave Resonance
Sign in / Sign up

Export Citation Format

Share Document