scholarly journals Perturbational Blowup Solutions to the Two-Component Dullin-Gottwald-Holm System

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Ka Luen Cheung
Keyword(s):  
Global Existence ◽  
Exact Solutions ◽  
Two Component

We construct a family of nonradially symmetric exact solutions for the two-component DGH system by the perturbational method. Depending on the parameters, the class of solutions includes both blowup type and global existence type.

Families of Exact Solutions for Two-Component Bose-Einstein Condensates

2010 ◽  
Vol 152-153 ◽  
pp. 1309-1312
Author(s):  
Dong Bo Cao ◽  
Liu Xian Pan ◽  
Yan Bin Sun ◽  
Jia Ren Yan
Keyword(s):  
Exact Solutions ◽  
Fiber Optics ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Transform Method ◽  
Two Component ◽  
Trigonometric Function Solutions ◽  
Bose Einstein

Two-component Bose-Einstein condensates systems are investigated in the presented work, using the trigonometric function transform method, and several families of exact solutions are obtained for coupled two-component nonlinear Gross Pitaevskii equations. The solutions obtained in this paper include four kinds of soliton solutions and five kinds of trigonometric function solutions. Finally, the corresponding exact solutions of the uncoupled NLS equations are easy derived in fiber optics.

Exact solutions of a two-component BEC interacting with a lattice potential

2005 ◽  
Vol 71 (1) ◽  
pp. 28-34 ◽  
Author(s):  
W Hai ◽  
Y Li ◽  
B Xia ◽  
X Luo
Keyword(s):  
Exact Solutions ◽  
Lattice Potential ◽  
Two Component

scholarly journals New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1984
Author(s):  
Roman Cherniha ◽  
Vasyl’ Davydovych
Keyword(s):  
Population Dynamics ◽  
Mathematical Models ◽  
Exact Solutions ◽  
Explicit Form ◽  
Volterra System ◽  
Two Component ◽  
Nonclassical Symmetries ◽  
Enormous Number

The diffusive Lotka–Volterra system arising in an enormous number of mathematical models in biology, physics, ecology, chemistry and society is under study. New Q-conditional (nonclassical) symmetries are derived and applied to search for exact solutions in an explicit form. A family of exact solutions is examined in detail in order to provide an application for describing the competition of two species in population dynamics. The results obtained are compared with those published earlier as well.

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