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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2604.19277 |
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| _version_ | 1866911611716894720 |
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| author | Carreño-Navas, Fernando Peñaranda, Siannah Alvarez-Nodarse, Renato Quintero, Niurka R. |
| author_facet | Carreño-Navas, Fernando Peñaranda, Siannah Alvarez-Nodarse, Renato Quintero, Niurka R. |
| contents | We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\barΨ\,Ψ|^{k}\,Ψ$ for positive values of $k$.
The system's energy is conserved despite the presence of a gain-loss term, which is quantified by the parameter $Λ$. We show that the $\PTb$-transition point is defined by the solution's existence condition and is independent of the nonlinearity exponent $k$. Furthermore, momentum is conserved, although neither the canonical momentum nor the charge is a conserved quantity. A notable result is that the stationary solution, obtained from the continuity equations, exhibits nonzero momentum in its rest frame. We also derive a moving soliton solution, where the gain-loss parameter allows the soliton's velocity to be precisely chosen so that the moving soliton possesses zero momentum. Finally, we establish that the presence of a gain-loss mechanism and higher-order nonlinearity restrict the stability domain of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized PT-symmetric nonlinear Dirac equation: exact solitary waves solutions, stability and conservation laws Carreño-Navas, Fernando Peñaranda, Siannah Alvarez-Nodarse, Renato Quintero, Niurka R. Pattern Formation and Solitons High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\barΨ\,Ψ|^{k}\,Ψ$ for positive values of $k$. The system's energy is conserved despite the presence of a gain-loss term, which is quantified by the parameter $Λ$. We show that the $\PTb$-transition point is defined by the solution's existence condition and is independent of the nonlinearity exponent $k$. Furthermore, momentum is conserved, although neither the canonical momentum nor the charge is a conserved quantity. A notable result is that the stationary solution, obtained from the continuity equations, exhibits nonzero momentum in its rest frame. We also derive a moving soliton solution, where the gain-loss parameter allows the soliton's velocity to be precisely chosen so that the moving soliton possesses zero momentum. Finally, we establish that the presence of a gain-loss mechanism and higher-order nonlinearity restrict the stability domain of the solutions. |
| title | Generalized PT-symmetric nonlinear Dirac equation: exact solitary waves solutions, stability and conservation laws |
| topic | Pattern Formation and Solitons High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.19277 |