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Math Help - Homogeneous Helmholtz Equation with Variable Coefficient

  1. #1
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    Question Homogeneous Helmholtz Equation with Variable Coefficient

    Hello,

    How does one go about solving a two dimensional (or more) homogeneous helmholtz equation with a variable coefficient, i.e.

    \Deltau(x,y) + u(x,y)*f(x,y) = 0

    Where in the standard Helmholtz equation, f(x,y) = k (constant). Knowing some boundary conditions. I am at a loss as to what method to even use, having tried separation of variables, green's functions, method of characteristics. Any hints? Can this equation even be solved?


    Thank You
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  2. #2
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    Is f(x,y) arbitrary or does it have a specific form?
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  3. #3
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    Quote Originally Posted by Danny View Post
    Is f(x,y) arbitrary or does it have a specific form?
    Nope, it's arbitrary. That's a good sign... right?
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  4. #4
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    It is possible that f(x,y) could be a number of step functions. Would that improve the situation?
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