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Family of KdV-type Equations

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Partial Differential Equations and Solitary Waves Theory

Part of the book series: Nonlinear Physical Science ((NPS))

Abstract

In this chapter we will study a family of KdV-type equations. These equations. These equations appear in many scientific fields as will be examined for each model. This family of KdV-type equations contains the following forms:

  1. (i)

    The complex modified KdV equation [16] (CMKdV) is of the form

    $$ w_t+ w_{xxx}+ \alpha (|w|^2 w)_x= 0, $$
    (15.1)

    where w is a complex valued function of the spatial coordinate x and the time t, and αis a real constant.

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Authors and Affiliations

  1. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

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  1. Abdul-Majid Wazwaz
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© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Wazwaz, AM. (2009). Family of KdV-type Equations. In: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00251-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-00251-9_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00250-2

  • Online ISBN: 978-3-642-00251-9

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