46 citations · 235 across the 24 of their papers we have counts for
25 papers
Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reduction
Almudena del Pilar Márquez, Elena Recio, María Luz Gandarias
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a…
On symmetries and conservation laws of a Gardner equation involving arbitrary functions
Rafael de la Rosa, María Luz Gandarias, María de los Santos Bruzón
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by u…
Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping
Rafael de la Rosa, María Luz Gandarias, María de los Santos Bruzón
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear dif…
Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation
Rafael de la Rosa, María Luz Gandarias, María de los Santos Bruzón
In this paper we study the generalized variable-coefficient Gardner equations of the form . This class broadens ou…
Exact solutions and conservation lawsof a one-dimensional PDE model for a blood vessel
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido +1
Two aspects of a widely used 1D model of blood flow in a single blood vessel are studied by symmetry analysis, where the variables in the model are the blood pressure and the cross…
Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido +1
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-…
Conservation laws, symmetries, and line solitons of a Kawahara-KP equation
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries a…
Conservation laws and variational structure of damped nonlinear wave equations
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido +1
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations…
Symmetries, conservation laws, and generalized travelling waves for a forced Ostrovsky equation
Stephen C. Anco, Maria Gandarias
Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classif…
Nonlinearly dispersive KP equations with new compacton solutions
Stephen C. Anco, Maria Gandarias
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher sp…
Symmetry multi-reduction method for partial differential equations with conservation laws
Stephen C. Anco, Mariluz Gandarias
For partial differential equations (PDEs) that have independent variables and a symmetry algebra of dimension at least , an explicit algorithmic method is presented f…
Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions
Stephen C. Anco, M. L. Gandarias, Elena Recio
A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Spe…
Conservation laws and line soliton solutions of a family of modified KP equations
Stephen C. Anco, M. L. Gandarias, Elena Recio
A family of modified Kadomtsev-Petviashvili equations (mKP) in 2+1 dimensions is studied. This family includes the integrable mKP equation when the coefficients of the nonlinear te…
Global versus local superintegrability of nonlinear oscillators
Stephen C. Anco, Angel Ballesteros, Maria Luz Gandarias
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetr…
Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions
S. C. Anco, M. L. Gandarias, E. Recio
Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with -power nonlinearities, arise in many physical applications and…
Conservation laws and symmetries of time-dependent generalized KdV equations
Stephen Anco, Maria Rosa, Maria Gandarias
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equation…
Conservation laws and symmetries of a generalized Kawahara equation
Maria Luz Gandarias, Maria Rosa, Elena Recio +1
The generalized Kawahara equation appears in many physical applications. A complete classification of low-order conservation laws an…
A nonlinear generalization of the Camassa-Holm equation with peakon solutions
Stephen C. Anco, Elena Recio, Maria L. Gandarias +1
A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power , is considered. This equation reduces to the Camassa-Holm equation when …
Analytic study of a coupled Kerr-SBS system
Robert Conte, Maria Luz Gandarias
In order to describe the coupling between the Kerr nonlinearity and the stimulated Brillouin scattering, Mauger et alii recently proposed a system of partial differential equations…
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
M. S. Bruzon, M. L. Gandarias, M. Senthilvelan
We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal sy…
Classical Lie symmetries and reductions of a nonisospectral Lax pair
P. G. Estevez, M. L. Gandarias, J. de Lucas
The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998),…
1+1 spectral problems arising from the Manakov-Santini system
M. S. Bruzon, P. G. Estevez, M. L. Gandarias +1
This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from th…
Symmetry reductions of a particular set of equations of associativity in twodimensional topological field theory
Robert Conte, Maria Luz Gandarias
The WDVV equations of associativity arising in twodimensional topological field theory can be represented, in the simplest nontrivial case, by a single third order equation of the…
Similarity reductions for a nonlinear diffusion equation
Maria Luz Gandarias, P. Venero, José Ramírez-Labrador
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial dif…