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1.1 Find the dispersion relation for the propagation of plane har- monic waves in the systems ди อน (a) i + = 0 ât @x2 (
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1.1 Find the dispersion relation for the propagation of plane har- monic waves in the systems ди อน (a) i + = 0 ât @x2 (
1.1 Find the dispersion relation for the propagation of plane har- monic waves in the systems ди อน (a) i + = 0 ât @x2 (the free space Schrödinger equation, which arises in quan- tum mechanics), дф (b) дф аф + 0 B де дх 2x3 - Vaxs (the linearised fifth order KDV equation). In each case, determine both the phase and group velocities. For each equation, determine p(x,t) if (x,0) = 8(x). Use the method of stationary phase to find an approximation to this solution for > 1 with v = x/t=0(1), v constant. a30
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