Doubt from waves


Is this equation of wave?

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At t=0 graph is discontinuous at x=0 thus it cannot be wave as a wave by property cannot be discontinuous.

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For any equation of the form y=f(x,t) to signify the wave phenomenon, it should be continuous for all values of x,t as we as, it should satisfy the wave equation : \nabla^2f=\frac{1}{v^2}\frac{\partial^2 f}{\partial t^2}, where the left hand side \nabla^2 is the laplacian operator, equivalent to \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}. One additional thing is that, in the limiting case when x\to\infty or t\to\infty the function should not diverge.

The asked function is not continuous for x=0,t=0 and so, it could not signify the wave phenomenon.


Only and only condition of wave is ,
Partial diff of y wrt t equals - × v× partial diff of y wrt x