Nonlinear Dynamics

, Volume 90, Issue 4, pp 2903–2915 | Cite as

Lie symmetry analysis, soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation

  • Vikas KumarEmail author
  • Aisha Alqahtani
Original Paper


In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV–Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge–Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV–Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.


Coupled KdV–Burgers equation Lie symmetry analysis Soliton solution Numerical solution 



The authors would like to thank the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University for supporting this research.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of MathematicsD.A.V. College PundariKaithalIndia
  2. 2.Department of Mathematical Sciences, College of SciencesPrincess Nourah bint Abdulrahman UniversityRiyadhSaudi Arabia

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