A new family of solitons for nonlinear Schrödinger equations with non-vanishing boundary conditions in high dimension
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917286131007488 |
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| author | Duan, Xiuqing |
| author_facet | Duan, Xiuqing |
| contents | In space dimensions $N \geq 4$, we introduce a new minimization procedure to construct traveling wave solutions to nonlinear Schrödinger equations with non-vanishing boundary conditions at spatial infinity. We denote the family of solitons obtained using this construction by $\mathscr{J}$. Mariş (Ann. of Math. 178:107-182, 2013) obtained a family of solitons by minimizing the action functional subject to a Pohozaev constraint; we use $\mathscr{P}$ to denote this family of solitons. Chiron and Mariş (Arch. Rational Mech. Anal. 226:143-242, 2017) used minimizing energy at fixed momentum to obtain a family of solitons; we denote this family of solitons by $\mathscr{Q}$. We show that, under some conditions, we have $\mathscr{Q} \subset \mathscr{J} \subset \mathscr{P}$. In addition, we show that $\mathscr{P} \subset \mathscr{J}$ under specific conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new family of solitons for nonlinear Schrödinger equations with non-vanishing boundary conditions in high dimension Duan, Xiuqing Analysis of PDEs 35Q51, 35Q55, 35Q40, 35J20 In space dimensions $N \geq 4$, we introduce a new minimization procedure to construct traveling wave solutions to nonlinear Schrödinger equations with non-vanishing boundary conditions at spatial infinity. We denote the family of solitons obtained using this construction by $\mathscr{J}$. Mariş (Ann. of Math. 178:107-182, 2013) obtained a family of solitons by minimizing the action functional subject to a Pohozaev constraint; we use $\mathscr{P}$ to denote this family of solitons. Chiron and Mariş (Arch. Rational Mech. Anal. 226:143-242, 2017) used minimizing energy at fixed momentum to obtain a family of solitons; we denote this family of solitons by $\mathscr{Q}$. We show that, under some conditions, we have $\mathscr{Q} \subset \mathscr{J} \subset \mathscr{P}$. In addition, we show that $\mathscr{P} \subset \mathscr{J}$ under specific conditions. |
| title | A new family of solitons for nonlinear Schrödinger equations with non-vanishing boundary conditions in high dimension |
| topic | Analysis of PDEs 35Q51, 35Q55, 35Q40, 35J20 |
| url | https://arxiv.org/abs/2602.18691 |