Response Solution to Ill-Posed Boussinesq Equation with Quasi-Periodic Forcing of Liouvillean Frequency

2019 ◽  
Vol 30 (2) ◽  
pp. 657-710 ◽  
Author(s):  
Fenfen Wang ◽  
Hongyu Cheng ◽  
Jianguo Si
Keyword(s):  
Boussinesq Equation ◽  
Periodic Forcing ◽  
Ill Posed ◽  
Liouvillean Frequency

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science

2017 ◽  
Vol 7 (3) ◽  
pp. 240-247 ◽  
Author(s):  
Serbay Duran ◽  
Muzaffer Askin ◽  
Tukur Abdulkadir Sulaiman
Keyword(s):  
Exponential Function ◽  
Physical Science ◽  
Function Method ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Nonlinear Media ◽  
Wolfram Mathematica ◽  
Ill Posed ◽  
Exponential Function Method

In manuscript, with the help of the Wolfram Mathematica 9, we employ the modified exponential function method in obtaining some new soliton solutions to the ill-posed Boussinesq equation arising in nonlinear media. Results obtained with use of technique, and also, surfaces for soliton solutions are given. We also plot the 3D and 2D of each solution obtained in this study by using the same program in the Wolfram Mathematica 9.

Auxiliary equation method for ill-posed Boussinesq equation

2019 ◽  
Vol 94 (8) ◽  
pp. 085213 ◽  
Author(s):  
Sadaf Bibi ◽  
Naveed Ahmed ◽  
Umar Khan ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boussinesq Equation ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Ill Posed

Dynamics of solitons to the ill-posed Boussinesq equation

2017 ◽  
Vol 132 (3) ◽  
Author(s):  
Fairouz Tchier ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Mustafa Inc
Keyword(s):  
Boussinesq Equation ◽  
Ill Posed

scholarly journals Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing

2017 ◽  
Vol 22 (6) ◽  
pp. 2501-2519 ◽  
Author(s):  
Yanling Shi ◽  
◽  
Junxiang Xu ◽  
Xindong Xu ◽  
Keyword(s):  
Periodic Solutions ◽  
Boussinesq Equation ◽  
Periodic Forcing ◽  
Generalized Boussinesq Equation

scholarly journals Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

2017 ◽  
Vol 228 (1) ◽  
pp. 129-157 ◽  
Author(s):  
Roberto Castelli ◽  
Marcio Gameiro ◽  
Jean-Philippe Lessard
Keyword(s):  
Periodic Orbits ◽  
Boussinesq Equation ◽  
Rigorous Numerics ◽  
Ill Posed
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