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Numerical solution of a highly nonlinear PDE and the absence of the soliton solution
Posted 27 giu 2020, 07:56 GMT-4 General, Acoustics & Vibrations, Equation-Based Modeling Version 5.3 3 Replies
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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.
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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
Please login with a confirmed email address before reporting spam
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?
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Yes, you can provide a function for the initial guess.
Best,
Jeff.
-------------------Jeff Hiller