A computational procedure for exact solutions of Burgers' hierarchy of nonlinear partial differential equations

DOI10.1007/s12190-020-01403-xOpenAlexW3042441222MaRDI QIDQ2053157

Sameerah Jamal, U. Obaidullah

Publication date: 29 November 2021

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-020-01403-x

zbMATH Keywords

transformationsBurgers' equationnonlinear equationsconserved vectors

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear waves in solid mechanics (74J30) PDEs in connection with mechanics of deformable solids (35Q74) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (10)

On the formulaic solution of a \((n+1)\)th order differential equation ⋮ Diverse acoustic wave propagation to confirmable time–space fractional KP equation arising in dusty plasma ⋮ A terminal condition in linear bond-pricing under symmetry invariance ⋮ On the conservation laws, Lie symmetry analysis and power series solutions of a class of third-order polynomial evolution equations ⋮ Elastic two-kink, breather, multiple periodic, hybrid and half-/local-periodic kink solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves ⋮ One-dimensional optimal system and similarity transformations for the \(3+1\) Kudryashov-Sinelshchikov equation ⋮ Singularity analysis and analytic solutions for the Benney-Gjevik equations ⋮ pp-wave potential functions: A complete study using Noether symmetries ⋮ Lie symmetry analysis and conservation laws of non-linear (2+1) elastic wave equation ⋮ Unnamed Item

Cites Work

• New \textit{higher-order} conservation laws of some classes of wave and Gordon-type equations
• Generalization of the double reduction theory
• Exact solutions of equations for the Burgers hierarchy
• Double reduction of PDEs from the association of symmetries with conservation laws with applications
• Invariant measures for Burgers equation with stochastic forcing
• Relationship between symmetries and conservation laws
• On abundant new solutions of two fractional complex models
• Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms
• Analytical, semi-analytical, and numerical solutions for the Cahn-Allen equation
• Inelastic interaction and blowup new solutions of nonlinear and dispersive long gravity waves
• New solitons and kinks solutions to the Sharma-Tasso-Olver equation
• The Cauchy problem for the equation of the Burgers hierarchy
• On the exact and numerical solution of the time-delayed Burgers equation
• Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method
• Evolution equations possessing infinitely many symmetries
• Conservation of Hamiltonian using Continuous Galerkin Petrov time discretization scheme
• Conservation laws for a Boussinesq equation.
• Solutions of quasi-geostrophic turbulence in multi-layered configurations
• Travelling wave solutions to nonlinear evolution and wave equations
• ON EXPLICIT WAVE SOLUTIONS OF THE FRACTIONAL NONLINEAR DSW SYSTEM VIA THE MODIFIED KHATER METHOD
• ON THE NEW EXPLICIT SOLUTIONS OF THE FRACTIONAL NONLINEAR SPACE-TIME NUCLEAR MODEL
• Remarks on the Burgers Equation
• Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves
• The partial differential equation u_t + uu_x = μ_xx

This page was built for publication: A computational procedure for exact solutions of Burgers' hierarchy of nonlinear partial differential equations