45 citations · 127 across the 14 of their papers we have counts for
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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…
Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs
Stephen C. Anco, Elena Recio
Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown…
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…
Accelerating dynamical peakons and their behaviour
Stephen C. Anco, Elena Recio
A wide class of nonlinear dispersive wave equations are shown to possess a novel type of peakon solution in which the amplitude and speed of the peakon are time-dependent. These no…
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…