In many systems, F ( p ^ ^ , p ^ ^ ′ ) only slowly depends on the angle between p ^ ^ and p ^ ^ ′ . If F is an angle-independent constant F 0 with F 0 > 0 (note that this constraint is stricter than the Pomeranchuk instability) then the wave has the form ν ν ( p ^ ^ ) ∝ ∝ ( ω ω / ( v F p ^ ^ ⋅ ⋅ k → → ) − − 1 ) − − 1 and dispersion relation s 2 log ⁡ ⁡ s + 1 s − − 1 − − 1 = 1 / F 0 where s = ω ω / k v F is the ratio of zero sound phase velocity to Fermi velocity. If the first two Legendre components of the Landau parameter are significant, F ( p ^ ^ , p ^ ^ ′ ) = F 0 + F 1 p ^ ^ ⋅ ⋅ p ^ ^ ′ and F 1 > 6 , the system also admits an asymmetric zero sound wave solution ν ν ( p ^ ^ ) ∝ ∝ sin ⁡ ⁡ ( 2 θ θ ) / ( s − − cos ⁡ ⁡ θ θ ) e i ϕ ϕ (where ϕ ϕ and θ θ are the azimuthal and polar angle of p ^ ^ about the propagation direction k ^ ^ ) and dispersion relation