Bifurcation analysis of generalized damped forced KDV equation and its analytical solitary wave solutions
In the present study, we investigate a generalized form of the Korteweg–de Vries (KdV) equation which is given by ut + Punux + Quxxx = 0. The analytical solution is generated using the sine-cosine method, which produces multi-solitons for different values of the parameters involved. The effects of t...
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| creator | Tomar, Shruti Chadha, Naresh M. Raut, Santanu |
| description | In the present study, we investigate a generalized form of the Korteweg–de Vries (KdV) equation which is given by ut + Punux + Quxxx = 0. The analytical solution is generated using the sine-cosine method, which produces multi-solitons for different values of the parameters involved. The effects of the non-linear coefficient (P), dispersion parameter (Q), and the exponent ’n ’ on to the solitons have been studied. Furthermore, the generalized KdV equation is modified to generalized damped forced KdV (DFKdV equation given by ut + Punux + Quxxx + Su = f (t), where additional damping term Su and forcing term f have been introduced. For this DFKdV, a few standard components such as phase portraits and Lyapunov exponents from the bifurcation theory of planar dynamical systems [4] have been employed to discuss various conditions on the parameters for the existence of the various types of solutions including chaos. |
| doi_str_mv | 10.1063/5.0164770 |
| format | Conference Proceeding |
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The analytical solution is generated using the sine-cosine method, which produces multi-solitons for different values of the parameters involved. The effects of the non-linear coefficient (P), dispersion parameter (Q), and the exponent ’n ’ on to the solitons have been studied. Furthermore, the generalized KdV equation is modified to generalized damped forced KdV (DFKdV equation given by ut + Punux + Quxxx + Su = f (t), where additional damping term Su and forcing term f have been introduced. 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The analytical solution is generated using the sine-cosine method, which produces multi-solitons for different values of the parameters involved. The effects of the non-linear coefficient (P), dispersion parameter (Q), and the exponent ’n ’ on to the solitons have been studied. Furthermore, the generalized KdV equation is modified to generalized damped forced KdV (DFKdV equation given by ut + Punux + Quxxx + Su = f (t), where additional damping term Su and forcing term f have been introduced. For this DFKdV, a few standard components such as phase portraits and Lyapunov exponents from the bifurcation theory of planar dynamical systems [4] have been employed to discuss various conditions on the parameters for the existence of the various types of solutions including chaos.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0164770</doi><tpages>12</tpages></addata></record> |
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| source | AIP Journals Complete |
| subjects | Bifurcation theory Damping Exact solutions Korteweg-Devries equation Liapunov exponents Mathematical analysis Parameters Solitary waves Standard components Trigonometric functions |
| title | Bifurcation analysis of generalized damped forced KDV equation and its analytical solitary wave solutions |
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