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Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation

Author

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  • Alvaro H. Salas
  • Cesar A. Gómez S.

Abstract

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole-Hopf transformation.

Suggested Citation

  • Alvaro H. Salas & Cesar A. Gómez S., 2010. "Application of the Cole-Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh-Order KdV Equation," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-14, March.
    • Handle: RePEc:hin:jnlmpe:194329
    DOI: 10.1155/2010/194329
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    Cited by:

    1. Xiaoming Wang & Shehbaz Ahmad Javed & Abdul Majeed & Mohsin Kamran & Muhammad Abbas, 2022. "Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. M. Ali Akbar & Md. Nur Alam & Md. Golam Hafez, 2016. "Application of the novel (G′/G)-expansion method to construct traveling wave solutions to the positive Gardner-KP equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 85-96, March.
    3. Hashtroud, A.M. & Ghamari, Danial & Moghimi-Araghi, Saman, 2020. "The crossover phenomena in surface growth models with height-dependent noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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