Numerical solution of a highly nonlinear PDE and the absence of the soliton solution

Please login with a confirmed email address before reporting spam

Hello. I try to solve the fourth order stationary PDE equation:

for right trangle geometry.

Following the procedure here and introducing and I rewrite the equation for the simulation

This equation can be represented as a General form PDE for the variables u, P, and Q: Gamma1=(ux+Px+Qx+1/3(ux)^3+ux(uy)^2), uy+Qy+1/3(uy)^3+uy(ux)^2) and F1=0;

Gamma2=(ux,0) and F2=P;

Gamma3=(0,uy) and F3=Q,

where all coefficients are equal to 1.

The equation is supplemented by Dirichlet conditions on the boundaries u=0 and the second derivatives uxx=0, uyy=0 also. Of course also I can introduce Neumann conditions.

It is well-known that for some approximations the equation gives rise soliton solution similar to a solution of the nonlinear Schrodinger equation. However and this is my problem after the Comsol simulation I obtain an obvious trivial solution with u=0. How to avoid this numerical solution? Is it possible? Thank you in advance.


3 Replies Last Post Jun 29, 2020, 1:11 PM EDT
Jeff Hiller COMSOL Employee

Please login with a confirmed email address before reporting spam

Posted: 2 weeks ago Jun 29, 2020, 9:17 AM EDT

Hello Yuriy,

You can influence which solution the solver goes towards by providing a suitable initial guess using the Initial Values node. The default Initial Values is zero, so if zero is a trivial solution and you don't override the default Initial Values, that's what the solver will find.

Best regards,

Jeff

-------------------
Jeff Hiller
Hello Yuriy, You can influence which solution the solver goes towards by providing a suitable initial guess using the Initial Values node. The default Initial Values is zero, so if zero is a trivial solution and you don't override the default Initial Values, that's what the solver will find. Best regards, Jeff

Please login with a confirmed email address before reporting spam

Posted: 2 weeks ago Jun 29, 2020, 11:06 AM EDT

Hello Yuriy,

You can influence which solution the solver goes towards by providing a suitable initial guess using the Initial Values node. The default Initial Values is zero, so if zero is a trivial solution and you don't override the default Initial Values, that's what the solver will find.

Best regards,

Jeff

Many thanks for the reply. Sure, I have played with initial guesses (values) that are different from zero. Nevertheless, I again obtain the zero solution eventually. If I'm not mistaken I can use also an initial function instead of a numerical value, am I correct?

>Hello Yuriy, > >You can influence which solution the solver goes towards by providing a suitable initial guess using the Initial Values node. The default Initial Values is zero, so if zero is a trivial solution and you don't override the default Initial Values, that's what the solver will find. > >Best regards, > >Jeff Many thanks for the reply. Sure, I have played with initial guesses (values) that are different from zero. Nevertheless, I again obtain the zero solution eventually. If I'm not mistaken I can use also an initial function instead of a numerical value, am I correct?

Jeff Hiller COMSOL Employee

Please login with a confirmed email address before reporting spam

Posted: 2 weeks ago Jun 29, 2020, 1:11 PM EDT

Yes, you can provide a function for the initial guess.

Best,

Jeff.

-------------------
Jeff Hiller
Yes, you can provide a function for the initial guess. Best, Jeff.

Reply

Please read the discussion forum rules before posting.

Please log in to post a reply.

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.