Results 41 to 50 of about 3,171,507 (251)

Classical and nonclassical symmetries of a generalized Boussinesq equation

, 1997
We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case.
Bluman G.W., Bluman G.W., Boussinesq J., Clarkson P.A., Gandarias M.L., Liu Y., Olver P.J., Olver P.J., Olver P.J., Ovsiannikov L.V.   +9 more
core   +1 more source

Derivation of the Camassa-Holm equations for elastic waves [PDF]

, 2015
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium.
Erbay, Husnu Ata, Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, Albert   +3 more
core   +1 more source

New Multiple Solution to the Boussinesq Equation and the Burgers-Like Equation

Journal of Applied Mathematics, 2013
By considering an improved tanh function method, we found some exact solutions of Boussinesq and Burgers-like equations. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions.
Hasan Bulut, Münevver Tuz, Tolga Akturk
doaj   +1 more source

Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation

Frontiers in Physics, 2023
In this work, we present two finite-dimensional Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation by using the nonlinearization method. Moreover, the separation of variables on the common level set of Casimir
Xue Geng, Dianlou Du, Xianguo Geng
doaj   +1 more source

Pseudospectral Method for the "Good" Boussinesq Equation [PDF]

Mathematics of Computation, 1991
The paper deals with the pseudospectral time-discrete method for the ''good'' Boussinesq equation. The difficulties in the study of the stability of the aliasing error in the nonlinear term are removed in a way which is roughly equivalent to the use of negative Sobolev norms. Numerical comparisons with finite difference schemes are also given.
de Frutos, J., Ortega, T., Sanz-Serna, J. M.   +2 more
openaire   +2 more sources

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

Open Physics, 2016
In 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.
Yaşar Emrullah, San Sait, Özkan Yeşim Sağlam   +2 more
doaj   +1 more source

Numerical Simulation and Analysis of Heat Transfer Characteristics in Gradient‐Porosity Foam Copper Composite Phase Change Materials

Energy Science &Engineering, EarlyView.
This study investigates the heat transfer characteristics of copper‐foam composite phase change materials with different gradient porosities. Three models with uniform porosity and three models with gradient porosities are developed to examine their effects on temperature distribution and melting behavior. ABSTRACT Phase change materials (PCMs) exhibit
Wei Yang, Chenchen Bao, Guofeng Zhou, Yuxi Qiao, Ruiling Yu, Manfeng Li, Linlin Zhang   +6 more
wiley   +1 more source

Conservation laws for a Boussinesq equation.

Applied Mathematics and Nonlinear Sciences, 2017
Abstract In this work, we study a generalized Boussinesq equation from the point of view of the Lie theory. We determine all the low-order conservation laws by using the multiplier method. Taking into account the relationship between symmetries and conservation laws and applying the multiplier method to a reduced ordinary differential
Gandarias, María Luz, Bruzón, María Santos   +1 more
openaire   +1 more source

Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion

International Journal for Numerical Methods in Fluids, EarlyView.
This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime, B. Després, M. A. Puscas, C. Fiorini   +3 more
wiley   +1 more source

The regularity properties and blow-up of the solutions for improved Boussinesq equations

Electronic Journal of Qualitative Theory of Differential Equations, 2021
In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence ...
Veli Shakhmurov, Rishad Shahmurov
doaj   +1 more source