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A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation

  • * Corresponding author: Muhammad Usman.

    * Corresponding author: Muhammad Usman. 
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  • In this work, we consider an ordinary differential equation obtained from a damped externally excited Korteweg de Vries-Kuramoto Sivashinsky (KdV-KS) type equation using traveling coordinates. We also include controls and delays and use an asymptotic perturbation method to analyze the stability of the traveling wave solutions. The existence of bounded solutions is presented as well. We consider the primary resonance defined by the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (discontinuous transitions between two stable solutions) for the KdV-KS type equation. We have obtained the existence of the bounded solutions of the system obtained from an ordinary differential equation associated with the KdV-KS equation and also show the global stability for a special case when there is no external force.

    Mathematics Subject Classification: Primary: 35B20, 35B32, 35B20, 35B32, 34Cxx, 37C75, 93Dxx, 34Exx.


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  • Figure 1.  Three solutions corresponding to $f=2.5$

    Figure 2.  External Excitation Response Curve

    Figure 3.  Frequency-Response Curve without delay

    Figure 4.  Frequency-Response Curve with varying B

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