### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 2903-2915 |

Number of pages | 13 |

Journal | Nonlinear Dynamics |

Volume | 90 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Dec 2017 |

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### Keywords

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

### Cite this

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*Nonlinear Dynamics*, vol. 90, no. 4, pp. 2903-2915. https://doi.org/10.1007/s11071-017-3851-0

**Lie symmetry analysis, soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation.** / Kumar, Vikas; Alqahtani, Aisha.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Lie symmetry analysis, soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation

AU - Kumar, Vikas

AU - Alqahtani, Aisha

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Coupled KdV–Burgers equation

KW - Lie symmetry analysis

KW - Numerical solution

KW - Soliton solution

UR - http://www.scopus.com/inward/record.url?scp=85031498158&partnerID=8YFLogxK

U2 - 10.1007/s11071-017-3851-0

DO - 10.1007/s11071-017-3851-0

M3 - Article

VL - 90

SP - 2903

EP - 2915

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -