Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids
Abstract The Korteweg de Vries-Burgers (KdV-B) (1+1) equation $$\begin{aligned} \frac{\partial \psi }{\partial t} +a \, \psi \frac{\partial \psi }{\partial x} + b \, \frac{\partial ^{3}\psi }{\partial x^{3}} = c \, \frac{\partial ^{2} \psi }{\partial x^2} \,, \end{aligned}$$ incorporating constant (...
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Nature Portfolio
2025-02-01
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| Online Access: | https://doi.org/10.1038/s41598-025-88432-3 |
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| author | Kuldeep Singh Steffy Sara Varghese Ioannis Kourakis |
| author_facet | Kuldeep Singh Steffy Sara Varghese Ioannis Kourakis |
| author_sort | Kuldeep Singh |
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| description | Abstract The Korteweg de Vries-Burgers (KdV-B) (1+1) equation $$\begin{aligned} \frac{\partial \psi }{\partial t} +a \, \psi \frac{\partial \psi }{\partial x} + b \, \frac{\partial ^{3}\psi }{\partial x^{3}} = c \, \frac{\partial ^{2} \psi }{\partial x^2} \,, \end{aligned}$$ incorporating constant (real) coefficients representing nonlinearity (a), dispersion (b) and dissipation (c), is a long known paradigm in e.g. plasma physics, where it can be derived from plasma fluid-dynamical models, so that all coefficients depend parametrically on the plasma composition. For a positive dispersion coefficient b (value), which is the general case in beam-free electron-ion plasma, this PDE possesses analytical solutions representing “shock”-shaped traveling waves with a characteristic kink (or anti-kink) soliton-like profile, for negative (or positive, respectively) values of the nonlinearity coefficient (a). In a plasma context, these excitations represent a monotonic transition between two (different) asymptotic values of the electrostatic potential $$\phi$$ , associated with a monopolar (i.e. bell-shaped) disturbance of the electric field (E). Contrary to widespread belief (based on a beam-free plasma description), an investigation of nonlinear electrostatic waves in beam-permeated plasmas reveals that the sign(s) of all (any) of the coefficients (a, b or c) may be reversed, independently from each other, depending on the beam velocity (value). In the light of this result, the analytical solutions have been reexamined in an effort to elucidate their applicability in plasma-physical scenarios (e.g., reconnection jets and other planetary plasma environments) in terms of the combined sign(s) of the various coefficients involved in the KdV-B equation. Different types of excitations are demonstrated to exist and the influence of the various coefficients on the solution’s propagation characteristics is examined. |
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| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nature Portfolio |
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| spelling | doaj-art-4d4d0d4c179140a6bec0c6ebe9beef4e2025-02-09T12:29:04ZengNature PortfolioScientific Reports2045-23222025-02-0115111310.1038/s41598-025-88432-3Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluidsKuldeep Singh0Steffy Sara Varghese1Ioannis Kourakis2Department of Mathematics, Khalifa University of Science & TechnologyDepartment of Physics, Amity University DubaiDepartment of Mathematics, Khalifa University of Science & TechnologyAbstract The Korteweg de Vries-Burgers (KdV-B) (1+1) equation $$\begin{aligned} \frac{\partial \psi }{\partial t} +a \, \psi \frac{\partial \psi }{\partial x} + b \, \frac{\partial ^{3}\psi }{\partial x^{3}} = c \, \frac{\partial ^{2} \psi }{\partial x^2} \,, \end{aligned}$$ incorporating constant (real) coefficients representing nonlinearity (a), dispersion (b) and dissipation (c), is a long known paradigm in e.g. plasma physics, where it can be derived from plasma fluid-dynamical models, so that all coefficients depend parametrically on the plasma composition. For a positive dispersion coefficient b (value), which is the general case in beam-free electron-ion plasma, this PDE possesses analytical solutions representing “shock”-shaped traveling waves with a characteristic kink (or anti-kink) soliton-like profile, for negative (or positive, respectively) values of the nonlinearity coefficient (a). In a plasma context, these excitations represent a monotonic transition between two (different) asymptotic values of the electrostatic potential $$\phi$$ , associated with a monopolar (i.e. bell-shaped) disturbance of the electric field (E). Contrary to widespread belief (based on a beam-free plasma description), an investigation of nonlinear electrostatic waves in beam-permeated plasmas reveals that the sign(s) of all (any) of the coefficients (a, b or c) may be reversed, independently from each other, depending on the beam velocity (value). In the light of this result, the analytical solutions have been reexamined in an effort to elucidate their applicability in plasma-physical scenarios (e.g., reconnection jets and other planetary plasma environments) in terms of the combined sign(s) of the various coefficients involved in the KdV-B equation. Different types of excitations are demonstrated to exist and the influence of the various coefficients on the solution’s propagation characteristics is examined.https://doi.org/10.1038/s41598-025-88432-3 |
| spellingShingle | Kuldeep Singh Steffy Sara Varghese Ioannis Kourakis Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids Scientific Reports |
| title | Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids |
| title_full | Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids |
| title_fullStr | Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids |
| title_full_unstemmed | Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids |
| title_short | Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids |
| title_sort | traveling wave solutions of a hybrid kdv burgers equation with arbitrary real coefficients in relation with beam permeated multi ion plasma fluids |
| url | https://doi.org/10.1038/s41598-025-88432-3 |
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