Travelling wave equation on one dimension to Gross Pitaeavkii equation is $$ \phi '' +ic\phi'+\phi (1-|\phi|^2)=0\qquad (1) $$ where $c\in (0,\sqrt{2})$ and $ \phi$ is a complex valued function. I am interested on the non-constant T-periodic solutions to equation (1). This post is just to know if someone could give me some notes, papers, books,... where I can read something about and if it is possible to know explicitly all the $T$-periodic solutions. Thanks in advance!

EDIT: I know $Ae^{icx}$ is a periodic solution whenever $|A|^2 =1$, but all of them have that form? How can I prove or disprove it?

Travelling wave equation on one dimension to Gross Pitaeavkii equation is $$ \phi '' +ic\phi'+\phi (1-|\phi|^2)=0\qquad (1) $$ where $c\in (0,\sqrt{2})$ and $ \phi$ is a complex valued function. I am interested on the non-constant T-periodic solutions to equation (1). This post is just to know if someone could give me some notes, papers, books,... where I can read something about and if it is possible to know explicitly all the $T$-periodic solutions. Thanks in advance!

Travelling wave equation on one dimension to Gross Pitaeavkii equation is $$ \phi '' +ic\phi'+\phi (1-|\phi|^2)=0\qquad (1) $$ where $c\in (0,\sqrt{2})$ and $ \phi$ is a complex valued function. I am interested on the non-constant T-periodic solutions to equation (1). This post is just to know if someone could give me some notes, papers, books,... where I can read something about and if it is possible to know explicitly all the $T$-periodic solutions. Thanks in advance!

Travelling wave equation on one dimension to Gross Pitaeavkii equation is $$ \phi '' +ic\phi'+\phi (1-|\phi|^2)=0\qquad (1) $$ where $c\in (0,\sqrt{2})$ and $ \phi$ is a complex valued function. I am interested on the non-constant T-periodic solutions to equation (1). This post is just to know if someone could give me some notes, papers, books,... where I can read something about and if it is possible to know explicitly all the $T$-periodic solutions. Thanks in advance!

EDIT: I know $Ae^{icx}$ is a periodic solution whenever $|A|^2 =1$, but all of them have that form? How can I prove or disprove it?