Constructing exact solutions for two-dimensional nonlinear dispersion Boussinesq equation. II: Solitary pattern solutions

2003 ◽  
Vol 18 (4) ◽  
pp. 869-880 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equation ◽  
Two Dimensional ◽  
Nonlinear Dispersion

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

Exact solutions of SL(N,R)‐invariant chiral equations one‐ and two‐dimensional subspaces

1992 ◽  
Vol 33 (10) ◽  
pp. 3521-3535 ◽  
Author(s):  
Tonatiuh Matos ◽  
Guadalupe Rodríguez ◽  
Ricardo Becerril
Keyword(s):  
Exact Solutions ◽  
Two Dimensional

scholarly journals Existence and Uniqueness Results for Two-Dimensional Stochastic Linearised Boussinesq Equation

2020 ◽  
Vol 6 (1) ◽  
pp. 20
Author(s):  
Sofije Hoxha ◽  
Fejzi Kolaneci
Keyword(s):  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Boussinesq Equation ◽  
Initial Condition ◽  
Two Dimensional ◽  
Boussinesq Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Drainable Porosity

The water flow in saturated zones of the soil is described by two-dimensional Boussinesq equation. This paper is devoted to investigating the linearised stochastic Boussinesq problem in the presence of randomness in hydraulic conductivity, drainable porosity, recharge, evapotranspiration, initial condition and boundary condition. We use the Sabolev spaces and Galerkin method. Under some suitable assumptions, we prove the existence and uniqueness results, as well as, the continuous dependence on the data for the solution of linearised stochastic Boussinesq problem. Keywords: linearised stochastic Boussinesq equation, Galerkin method, existence and uniqueness results, and continuous dependence on the data.

scholarly journals Nonclassical Symmetry Analysis of Boundary Layer Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Rehana Naz ◽  
Mohammad Danish Khan ◽  
Imran Naeem
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Similarity Solution ◽  
Symmetry Analysis ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Nonclassical Symmetry ◽  
Nonclassical Symmetries

The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.

scholarly journals On f(R) Theories in Two-Dimensional Spacetime

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
M. A. Ahmed
Keyword(s):  
Exact Solutions ◽  
Ricci Scalar ◽  
Two Dimensional ◽  
Field Equations ◽  
Dimensional Spacetime ◽  
Set Up

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained.

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