Wave shoaling and the angular frequency is proportional to its local rate of change, Simplifying to one dimension and cross-differentiating it is now easily seen that the above definitions indicate simply that the rate of change of wavenumber is balanced by the convergence of the frequency along a ray; Assuming stationary conditions (formula_27), this implies that wave crests are conserved and the frequency must remain constant along a wave ray as formula_28. As waves enter shallower waters, the decrease in group velocity caused by the reduction in water depth leads to a reduction in wave length formula_29 because the nondispersive shallow water
Zero sound transport equation is valid in the regime where formula_36 and formula_37. In many systems, formula_38 only slowly depends on the angle between formula_39 and formula_40. If formula_29 is an angle-independent constant formula_42 with formula_43 (note that this constraint is stricter than the Pomeranchuk instability) then the wave has the form formula_44 and dispersion relation formula_45 where formula_46 is the ratio of zero sound phase velocity to Fermi velocity. If the first two Legendre components of the Landau parameter are significant, formula_47 and formula_48, the system also admits an asymmetric zero sound wave solution formula_49 (where formula_50 and formula_51 are the